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There's a common phrase that's used, quantum computing tries every solution in parallel, and it finds the right answer.

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And I mean, like, kinda, but like, honestly, not really.

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Because if that were actually true, then every single problem ever could just be done

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on a quantum computer in parallel.

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This is a big argument when people talk about encryption.

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And encryption is maybe the only thing where it's true.

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Where it's actually true.

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Everything else, though, maybe not.

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What ends up happening is there's only very specific types of questions where you can exploit the properties of quantum mechanics.

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Hello, Internet.

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This is your captain speaking, Lester Nare, joined as always by my co-host and our resident PhD, Krishna Chowdhury.

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We are excited to start part one of what will be a two-part deep dive on quantum computing, covering the recent cover story in Nature, Volume 655, Issue 8125, released on July 30th, 2026, featuring our resident physicist Krishna as a co-author on the cover paper of Nature.

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We are very excited about this.

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This is going to be right in the wheelhouse of the show.

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And there was so much to talk about.

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We're going to spread it over two episodes.

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As always, we are going to talk about the science from the ground up today because this is from First Principles.

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Those of you who keep up with us on Instagram and watch our stories there will know that I am co-author on a paper that was recently published in Nature.

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And not only was it published, it was featured on the cover.

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And I have to say, when I was a PhD student at UCLA and I was in the intersection of neuroscience and physics, I definitely dream...

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about this day, right?

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Every PhD student dreams about the day that maybe one of their papers is going to be featured on the cover of Nature, Science, Cell, things like that.

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I wouldn't have guessed that it would have been a quantum computing story, though.

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And I think if you ask a PhD Krishna

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About it.

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He'd be like, wait, what happened to the original plot of the movie?

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You know?

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And also, why are you in a podcast studio?

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Anyway, so here's the paper itself.

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It's called A Digitally Controlled Silicon Quantum Processing Unit.

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There are a lot of authors.

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The official author that's like under the tagline there is...

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members of the HRL quantum team and collaborators.

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HRL labs is my former workplace and something like 250 authors are on this thing.

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And right there on the list in the blue, that's, that's me highlighted.

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It's an alphabetical order.

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So, you know, Chowdhury CH comes up maybe 20% down.

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If they actually did it in order of importance, I think I'd be somewhere in the bottom line there.

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Nobody has to know.

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You know, yeah, it still counts.

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It still counts.

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And there's a good reason why there are so many authors, because I think what we accomplished required a lot of manpower and a lot of resources.

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Yeah.

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We've covered stories before that have a lot of big groups.

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So this isn't like totally out of the ordinary or physics papers.

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For example, we've covered the Brookhaven's star collaboration when they were doing like some weird quark physics.

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Or the Event Horizon Telescope.

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That thing has 300 authors in all of its papers.

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That's the collaboration that images the black hole of M87.

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Even when you did the interview with Dr. Michael Blanton at Carnegie, he had mentioned this transition from individual name papers to sort of this idea of big science.

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Exactly.

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And he kind of lived through that transition.

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Yes, exactly.

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And to build a quantum computer, it requires big science.

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Now, I was planning to cover that paper, and then as I was cramming everything and doing all of my background research, I started realizing that in order to talk about...

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that paper and put it into context, a single episode is going to leave me unsatisfied.

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And more importantly, it's going to leave our audience unsatisfied because we have spoiled our audience with the history of the thing and then the contextualizing of the thing and then what the paper is and putting it in context with the broader world and blah, blah, blah.

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There's a lot

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That goes on in the quantum computing world, right?

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It's a whole new paradigm of computing.

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So you can imagine there's a theoretical side, there's a software side, and there's a hardware side.

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The paper that I'm co-author on is mostly a hardware paper.

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But in order to really understand why it's such a big deal...

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And why it's on the cover of nature.

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I think, you know, we need to put it into the context of this larger quantum computing ecosystem.

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I mean, there's so many competing technologies that are out there.

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There's trapped ions.

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There's neutral atoms.

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There's superconducting qubits.

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There's spins.

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That's the one that we're going to talk about.

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There's...

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Majorana modes there's from Microsoft I don't know why that's on there to be honest but we'll get into that a little bit later so there's all these storylines and to really appreciate it you need a lot of context first you need the context about what quantum computing is in general and why people should care.

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I hear about quantum.

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You know, there's Marvel movies that use the word quantum.

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Yeah.

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It was one of the worst Marvel movies, I think.

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The Ant-Man one, quantum something.

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Literally one of the worst.

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It's used as this rhetorical device for a lot of...

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different ideas that are totally unrelated to the actual scientific study.

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And so I think this was going to be really interesting.

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I see the quantum supremacy stuff from Google.

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All these headlines all the time.

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I don't know how to parse.

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I didn't even know that there were different types.

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I thought it was just all the same quantum.

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Yeah, yeah, yeah.

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And so this is, I think, is going to be interesting in helping to really distill down, like, what are we actually talking about?

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Exactly, yeah.

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And so that's what today's episode is about.

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We're going to talk about...

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The history of the field from a theory perspective.

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The next episode that's going to happen next week is when we're going to go into the hardware modalities and talk about how to actually build a working, scalable quantum computer.

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So the paper...

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is actually going to be next episode.

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This episode is the theoretical foundations and the setup for why we would even want to build something like this.

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If it's so hard, there better be a good reason for why we're building it, right?

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So the questions that we're going to answer here are things like, what is a qubit?

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What is a quantum algorithm?

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And I want to contrast today's multi-billion dollar technologies.

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I think now it's like in the trillions, to be honest, against the humble beginnings of this field.

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it's like countercultural beginnings in the 1960s, 70s, and 80s.

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We're going to focus a lot on some of the human stories behind it.

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Because at the time, people were thinking about quantum computing in their spare time.

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There was no research program when this thing started about quantum computing.

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Now there's like entire half of a department of physics that will just be doing quantum computing at certain universities.

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Right.

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So from humble beginnings to where we are now, it's a, it's a, it's an incredible story.

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I want to give our audience a sense of why everyone is so obsessed with building one.

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And, um, I want to dismantle the hype is another big thing that I want to do here because we, we hear a lot of hype about quantum.

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As you mentioned, it's an every Marvel movie, whenever they need some gimmick to like time travel or like teleport.

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Yeah, like Erase Memories, the new Spider-Man movie.

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I haven't watched it yet.

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I want to, but there's probably some quantum nonsense in there.

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So if you're not careful, you can get it wrong, right?

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The hype is definitely real, and it's definitely there.

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There's a common phrase that's used that quantum computing tries every solution in parallel, and it finds the right answer.

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And I mean, like, kind of, but honestly, not really.

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Because if that were actually true, if quantum computing was just like doing all of the solutions in parallel, then every single problem ever could just be done on a quantum computer in parallel.

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Every problem has a myriad of possible solutions.

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Okay, just try all of them in parallel, and then what?

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You just solve everything?

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So what, p doesn't equal np equals constant np?

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Right?

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Just constant time.

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You press it on a quantum computer, you're done.

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This is a big argument when people talk about encryption specifically.

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Yeah.

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And it's like, oh, what would take a trillion years can be run in parallel on a quantum computer and can be done in...

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Yeah.

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Seconds.

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And encryption is maybe the only thing.

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Where it's true.

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Where it's actually true.

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Everything else, though, maybe not, right?

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So that's kind of what I'm trying to get into.

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What ends up happening is there's only very specific types of questions where you can exploit the properties of quantum mechanics.

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Okay.

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Okay?

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And in this episode, we're going to explore one of the famous algorithms called the Deutsch-Joseph algorithm.

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It's probably the simplest algorithm to understand.

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I don't think it's very useful.

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except as a teaching tool to understand how quantum algorithms actually work.

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Okay.

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It's simple enough that I think I could do a good job on this podcast to explain at least some of the magic behind, um, why what's actually happening.

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And we will talk about Shor's algorithm.

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Don't worry about it, but, um, we're not going to like go into detail because that's going to require another full deep dive.

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I just have to say Deutsch, Deutsch, Josa sounds like a starter for Liverpool.

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Yeah.

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So that's the preview.

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Yep.

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All right.

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And now let's get into it.

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We begin in 1964 with the formulation of Bell's theorem.

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This is a photo of our America 250 timeline that we had prepared for the celebration of America's 250th birthday.

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We had done a giant timeline of some 400

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accomplishments that America was responsible for.

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A lot of people think that John Bell was mostly at CERN, but actually he took a one-year sabbatical and he came to the United States in 1964.

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He visited Stanford University and the University of Wisconsin.

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And during that sabbatical is when he wrote the seminal paper that he is most well-known for.

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It showed definitively that local hidden variables cannot account for the richness of the observed phenomenon that we see in quantum mechanics.

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So I want to dive a little bit into that because I think that is going to be the foundation for understanding why Feynman got into it.

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A lot of people just start with Feynman.

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There's a lot of stuff that happened before Feynman, okay?

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And I don't want to be a podcast that is the cult of Feynman.

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There's plenty out there.

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Feynman is a great man, as we will see in the talk that he gives.

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But there was a lot of stuff that happened before then that enabled him to think about those problems.

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And for anyone who actually is interested in checking out that America 250, you can go to ffppod.com backslash America 250.

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It's an interactive timeline that covers some of the stuff you just mentioned.

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That's pre-Findman, as well as many of the other great discoveries in our history.

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And it's, I think, a really humbling experience to go through it in that format.

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Yeah.

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And Feynman is mentioned a lot on that timeline because he did a lot of really cool things.

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So let's start with our entanglement experiment that everyone gets to know.

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Alice and Bob.

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Okay.

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They always use Alice and Bob.

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I don't know why.

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I think it's because A and B.

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Maybe if somebody has an idea of historically why we always use Alice and Bob in these entanglement thought experiments, please let us know.

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So here's the idea.

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Suppose I create two particles with spin, and they're entangled.

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So, I don't know, maybe like a photon goes through a crystal, and then it splits into two.

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So then the two photons that were created were created from the same quantum state, so they're going to have an entangled quantum state.

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Now, by conservation of angular momentum, if Alice gets one of these particles and Bob gets another one of these particles, and Alice observes her particle spinning one way, then by conservation of angular momentum,

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Bob should see his particle spinning the other direction, right?

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Because then the two spins cancel out.

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But according to quantum mechanics, there's a probability that Alice is going to see the spin going one way and the other way.

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And then a probability that Bob is going to see it going the other way.

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It's just that the two probabilities are correlated and that they always have to be opposite.

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Now, that begs the question, is there a spin to begin with?

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Right.

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Okay.

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That was like made in the entanglement state and then got split up.

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Okay.

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Or the alternative being, or is it only existent once it's been quote observed?

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Exactly.

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And that's Niels Bohr.

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Which is a complex.

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What is it?

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Yeah.

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What does that even mean?

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Right.

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So Niels Bohr is like, no, that second thing.

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No, that's it.

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Right.

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There's no well-defined spin.

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And then only when you observe it, the wave function collapses and,

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And then you get one direction or the other.

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Right?

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And Einstein's like, this is nonsense.

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This doesn't make any sense.

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He insisted on something called local realism because, one, he liked local because local means that nothing travels faster than speed of light, which makes sense.

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And the physical objects possess definite properties that are independent of observation.

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Okay?

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So that's like the realism part.

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And they can't propagate faster than the speed of light.

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There's no communication.

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Okay.

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So effectively, if you've seen the Denzel Washington movie, Deja Vu, he's effectively Denzel Washington.

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Okay.

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There's that really funny scene where like he's looking through a wormhole or something and he's asking if the person is alive.

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And one of the scientists is like, well, time is not a local variable.

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And then he's like, it's so funny.

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He's like, let me say it slow.

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Okay.

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So you PhDs can understand.

230
00:15:08.972 --> 00:15:09.433
Right.

231
00:15:09.533 --> 00:15:12.453
And then he takes a chair and destroys a monitor.

232
00:15:12.473 --> 00:15:14.974
And he's like, this monitor is now dead.

233
00:15:14.994 --> 00:15:19.835
It is not in a superposition of different entropy.

234
00:15:19.935 --> 00:15:20.915
And that's Einstein.

235
00:15:21.555 --> 00:15:23.135
It's such a classic scene.

236
00:15:23.275 --> 00:15:24.275
And it's a great movie.

237
00:15:24.695 --> 00:15:25.476
It is really good.

238
00:15:25.496 --> 00:15:30.317
And it touches on some of these subjects, maybe in some ways great, in some ways not so great.

239
00:15:30.477 --> 00:15:30.637
Yeah.

240
00:15:30.657 --> 00:15:32.297
But it quite, it quite.

241
00:15:32.897 --> 00:15:40.283
gives a real lived human experience to these theoretical questions in a way that you could try to kind of visualize.

242
00:15:40.423 --> 00:15:41.084
Yeah.

243
00:15:41.244 --> 00:15:49.451
And honestly, I was Denzel Washington before I just sort of succumbed to my fate and was like, okay, just shut up and calculate.

244
00:15:49.791 --> 00:15:52.554
But when you're first learning it, everyone is Denzel Washington.

245
00:15:52.854 --> 00:15:53.895
What are you talking about?

246
00:15:53.915 --> 00:15:54.095
Right.

247
00:15:54.335 --> 00:15:54.595
Right.

248
00:15:54.816 --> 00:15:55.156
So –

249
00:15:56.697 --> 00:16:04.319
Effectively, under local realism, any correlation that's observed between Alice and Bob have to do with some kind of hidden variable.

250
00:16:04.359 --> 00:16:11.561
This is the famous EPR Einstein-Pedolsky-Rosen paper that Einstein published in 1935.

251
00:16:11.921 --> 00:16:19.083
And he showed that if you have some kind of local hidden variable, then you can perhaps account for the...

252
00:16:20.443 --> 00:16:22.285
It could kind of make sense, right?

253
00:16:22.886 --> 00:16:25.428
And for the longest time, it was like, okay, fine, whatever.

254
00:16:25.809 --> 00:16:30.673
The local hidden variable takes place of the wave function collapsing during observation.

255
00:16:30.693 --> 00:16:30.974
Yeah, yeah.

256
00:16:31.014 --> 00:16:32.955
It's like there's something that's saved.

257
00:16:32.995 --> 00:16:38.601
There's like a saved attribute in the two particles that then we observe on either side.

258
00:16:38.881 --> 00:16:47.463
Now, crucially, when we only observe the spin in one direction, both the classical interpretation and the quantum interpretation are the same.

259
00:16:47.603 --> 00:16:47.843
Fine.

260
00:16:48.063 --> 00:16:48.263
Right?

261
00:16:48.623 --> 00:16:51.083
Because we're going to observe them in the opposite directions.

262
00:16:51.203 --> 00:16:54.784
And so for the longest time, it was like, oh, this is just like a philosophical argument.

263
00:16:54.804 --> 00:16:56.404
There's no way to prove it one way or the other.

264
00:16:56.444 --> 00:16:56.845
Who cares?

265
00:16:58.105 --> 00:17:00.205
Along comes John Graham Bell.

266
00:17:00.945 --> 00:17:01.165
Okay?

267
00:17:01.785 --> 00:17:04.226
John Graham Bell has the crucial insight in...

268
00:17:04.927 --> 00:17:10.309
this particular paper, I mean, it's literally called On the Einstein-Podolsky-Rosen Paradox.

269
00:17:10.509 --> 00:17:14.250
And crucially, the affiliation there is University of Wisconsin-Madison.

270
00:17:14.570 --> 00:17:18.171
So this is the paper for Bell's inequality, and it's in America.

271
00:17:19.451 --> 00:17:22.172
And that's why it's on our America 250, you know?

272
00:17:22.252 --> 00:17:26.453
It's like, hey, that one year, that one year was everything.

273
00:17:27.233 --> 00:17:32.335
So he realizes that we can actually expand the Alice and Bob experiment

274
00:17:33.678 --> 00:17:35.635
To give Alice and Bob a choice.

275
00:17:36.891 --> 00:17:50.680
instead of them only observing a single direction, we can maybe have a filter where they can observe the spin in the Z direction, up and down, or in the X direction, sideways.

276
00:17:50.960 --> 00:17:59.726
So when the light particle comes in, I can adjust my filter, my polarizer or whatever, to say, okay, what is the spin in the X direction?

277
00:17:59.746 --> 00:18:01.687
What is the spin in the Z direction?

278
00:18:02.147 --> 00:18:03.368
Now I've got two choices.

279
00:18:03.548 --> 00:18:06.010
Alice has the same choice and Bob has the same choice.

280
00:18:06.530 --> 00:18:12.053
And Alice is going to observe up and down in Z if she chose Z, or up and down in X if she chose X.

281
00:18:12.193 --> 00:18:15.015
And similarly, Bob has two choices as well.

282
00:18:15.435 --> 00:18:17.576
Now we sort of have this matrix of options.

283
00:18:17.756 --> 00:18:18.257
Exactly.

284
00:18:18.277 --> 00:18:18.677
Based on...

285
00:18:19.297 --> 00:18:22.979
Yes, now we have a matrix of options, and now we can actually disentangle.

286
00:18:24.140 --> 00:18:29.503
Is there a hidden variable, or is the quantum mechanics doing crazy nonsense?

287
00:18:29.983 --> 00:18:30.263
Okay?

288
00:18:30.864 --> 00:18:35.006
Bell shows that in the local realism world, Einstein's world,

289
00:18:36.527 --> 00:18:53.518
the joint conditional probability distributions of all of these outcomes, like the probability distribution of Alice observing this way, given that, and Bob observing this way, given his choice, it can factor out into two independent components that are local.

290
00:18:53.818 --> 00:18:54.078
Okay.

291
00:18:54.399 --> 00:19:01.263
If there's a hidden variable, I can factor it out into like this particle in Bob and that particle in Alice.

292
00:19:01.864 --> 00:19:02.124
Okay.

293
00:19:02.844 --> 00:19:03.365
On the other hand,

294
00:19:04.331 --> 00:19:12.255
Quantum mechanics predicts that there is going to be certain settings where the correlation is going to exceed that bound.

295
00:19:12.575 --> 00:19:15.416
If you could factor, the correlation can only go up a certain amount.

296
00:19:16.097 --> 00:19:19.579
But for certain angles, the correlation is actually going to exceed.

297
00:19:19.859 --> 00:19:24.001
So now you've got a way to prove one way or the other.

298
00:19:25.248 --> 00:19:27.212
is there a hidden variable or not?

299
00:19:27.512 --> 00:19:32.742
John Klauser very famously did this at Berkeley, another one in our America 250 timeline.

300
00:19:33.483 --> 00:19:35.287
And he showed that, in fact...

301
00:19:36.505 --> 00:19:37.425
There is a violation.

302
00:19:37.606 --> 00:19:37.786
Right.

303
00:19:37.986 --> 00:19:39.627
There is a violation of Bell's inequality.

304
00:19:39.907 --> 00:19:42.988
And you cannot factor this probability distribution.

305
00:19:43.389 --> 00:19:43.609
Okay.

306
00:19:43.849 --> 00:19:45.270
There's no separate components.

307
00:19:45.610 --> 00:19:50.813
You have to consider the entire thing in this giant, no matter how far apart Alice and Bob are.

308
00:19:51.273 --> 00:19:51.493
Okay.

309
00:19:51.893 --> 00:20:00.158
John Klauser did this in the – he won the 2022 Nobel Prize in Physics along with Alain Aspect and Anton Zeilinger.

310
00:20:00.178 --> 00:20:00.658
Mm-hmm.

311
00:20:01.864 --> 00:20:05.947
These guys were instrumental at taking Bell's inequality to the absolute limit.

312
00:20:06.307 --> 00:20:07.888
John Klauser was the first guy to do it.

313
00:20:08.348 --> 00:20:21.038
And these other two started considering very, very like, you know, whenever, whenever, whenever John Klauser did that, there's there's people that'll come up and be like, well, maybe the hidden variable is like in the lab.

314
00:20:21.738 --> 00:20:24.621
In the giant room that John Klauser is in.

315
00:20:24.681 --> 00:20:29.406
Because he's making these particles and then making it go to one end of the lab and the other end of the lab.

316
00:20:29.746 --> 00:20:32.589
His experiment was still kind of local.

317
00:20:32.629 --> 00:20:36.212
And then he's making choices that are local to him.

318
00:20:36.933 --> 00:20:38.595
He's choosing when to...

319
00:20:39.335 --> 00:21:02.750
put the polarizers in one direction or the other is the argument basically like the scope of what you're accounting for is is like still kind of local right right it's still kind of when is when does it not become yeah yeah so then alan aspect alan aspect i think one of his one of his amazing experiments he did actually i believe it was at tenerife in the observatories there tenerife has these amazing observatories um

320
00:21:03.930 --> 00:21:07.132
optical telescopes that are across the mountain, right?

321
00:21:07.512 --> 00:21:23.423
So now what you can do, the main problem with John Klauser's experiment was that he was kind of choosing, even with a random number generator, he was kind of choosing himself which way to set the polarizers, what choice to make for his Alice and his Bob.

322
00:21:23.904 --> 00:21:28.927
Alan Aspect said, okay, I'm going to point telescopes in opposite directions of the universe, right?

323
00:21:29.407 --> 00:21:35.972
One is going to point at a quasar that's like billions of light years this way, and one is going to point at a quasar a billion light years that way.

324
00:21:37.173 --> 00:21:43.938
And depending on the light from the quasars, the quasars are going to make the choice on which direction my polarizing filter is going to be.

325
00:21:45.561 --> 00:21:47.564
Bell's inequality is still violated.

326
00:21:48.005 --> 00:21:52.351
So that means that whatever local variable has to be like the size of the universe.

327
00:21:53.012 --> 00:21:56.276
At that point, it's like, what is local, right?

328
00:21:56.717 --> 00:22:01.844
And so just to say this back to you, the idea is like, who decides the position of the filter?

329
00:22:02.405 --> 00:22:08.027
initially was not considered sufficient to say that the hidden variable is not a thing.

330
00:22:08.207 --> 00:22:08.427
Yeah.

331
00:22:08.467 --> 00:22:14.029
Because the idea was the decider of that was still too local to the system of observation.

332
00:22:14.049 --> 00:22:14.249
Yeah.

333
00:22:14.529 --> 00:22:24.832
And so now when we utilize these distant celestial objects as the variable that decides what direction the filter is in, in this matrix of options...

334
00:22:26.485 --> 00:22:32.587
Now our experimental design is billions of light years across versus just whatever, a couple tens of yards or whatever.

335
00:22:32.987 --> 00:22:43.089
And so you're – and then the argument that this hidden variable can exist in this billion light years across experimental apparatus can no longer be considered reasonable.

336
00:22:43.169 --> 00:22:44.330
Yeah.

337
00:22:44.490 --> 00:22:47.731
And now we are able to – we still violate Bell's theorem.

338
00:22:48.751 --> 00:22:52.712
And so we – the realists – sorry.

339
00:22:52.732 --> 00:22:52.952
Yeah.

340
00:22:53.132 --> 00:22:53.852
Yeah, sorry.

341
00:22:53.872 --> 00:23:02.657
I mean, unless you're really like doubling down and you're saying there's just a universe wide local variable or something, you know, it's getting it's getting tenuous now.

342
00:23:03.057 --> 00:23:03.278
Right.

343
00:23:03.298 --> 00:23:05.038
Because now we're arguing over the definition of local.

344
00:23:05.099 --> 00:23:06.719
Yeah, yeah, yeah, exactly.

345
00:23:06.759 --> 00:23:06.960
Right.

346
00:23:07.580 --> 00:23:09.701
So the key thing here that I want you to take away.

347
00:23:09.721 --> 00:23:12.302
OK. Is that factoring capability.

348
00:23:12.583 --> 00:23:13.223
OK. OK.

349
00:23:13.483 --> 00:23:21.833
It means that you cannot factor the physics into separate components, one for Alice and her particle and one for Bob and his particle.

350
00:23:22.054 --> 00:23:27.641
Okay, that's the key thing that establishes that quantum mechanics is very, very weird.

351
00:23:28.442 --> 00:23:31.585
And that's the insight that Feynman uses in his 1981 talk.

352
00:23:33.007 --> 00:23:36.410
Can you maybe phrase it in a slightly different way?

353
00:23:36.450 --> 00:23:38.031
Because I think I understand what you're saying.

354
00:23:38.051 --> 00:23:50.983
When you say you can't factor it independently for both, are you trying to say that there's a rule set above when either of them observe or act in a system that is not independent of each other?

355
00:23:51.003 --> 00:23:51.523
So there's like –

356
00:23:54.196 --> 00:24:02.563
In order to really try and understand what is happening in this experiment, we have to consider the entire system at once.

357
00:24:03.164 --> 00:24:06.086
We cannot consider the systems separate.

358
00:24:06.467 --> 00:24:10.730
The particles cannot be considered in any mathematical form to be separate from one another.

359
00:24:10.830 --> 00:24:11.111
I see.

360
00:24:11.151 --> 00:24:16.035
They are connected by a single wave function is one way of putting it, right?

361
00:24:16.075 --> 00:24:18.197
Like the mathematics is inherently tied.

362
00:24:18.257 --> 00:24:19.158
It is one block.

363
00:24:19.318 --> 00:24:19.458
Yes.

364
00:24:19.478 --> 00:24:19.558
Yes.

365
00:24:19.778 --> 00:24:19.978
Right.

366
00:24:20.118 --> 00:24:21.899
It is a singular Lego block.

367
00:24:21.939 --> 00:24:24.999
You can't break it down into subsequent smaller Lego blocks.

368
00:24:25.039 --> 00:24:25.219
No.

369
00:24:25.319 --> 00:24:28.780
The whole system that you're observing at whatever scale.

370
00:24:28.900 --> 00:24:29.100
Yeah.

371
00:24:29.640 --> 00:24:32.661
Has to be considered a singular Lego block.

372
00:24:32.721 --> 00:24:32.861
Yes.

373
00:24:32.881 --> 00:24:33.561
In this analogy.

374
00:24:33.581 --> 00:24:33.781
Yeah.

375
00:24:33.821 --> 00:24:33.981
Yeah.

376
00:24:34.081 --> 00:24:36.742
In order to really capture all of the quantum mechanics that is happening.

377
00:24:36.762 --> 00:24:36.902
Okay.

378
00:24:36.922 --> 00:24:37.102
Okay.

379
00:24:37.342 --> 00:24:39.343
There's no way to be like there's a hidden variable.

380
00:24:39.383 --> 00:24:41.483
And so, you know, this guy has this thing saved.

381
00:24:41.543 --> 00:24:42.783
That guy has that thing saved.

382
00:24:42.864 --> 00:24:43.584
And so.

383
00:24:44.004 --> 00:24:44.264
Okay.

384
00:24:44.364 --> 00:24:44.884
You know what I mean?

385
00:24:44.904 --> 00:24:45.124
Yeah.

386
00:24:45.144 --> 00:24:45.244
Yeah.

387
00:24:45.324 --> 00:24:45.724
Okay.

388
00:24:45.784 --> 00:24:48.265
So that's the key insight that Feynman is going to use later in 1981.

389
00:24:48.285 --> 00:24:48.405
Okay.

390
00:24:48.425 --> 00:24:48.525
Okay.

391
00:24:49.205 --> 00:24:52.626
Now, this is in the 1960s, and we've got a long way to go before 1981, okay?

392
00:24:52.706 --> 00:24:55.066
Because there's a lot more stuff that happens.

393
00:24:55.206 --> 00:25:01.368
In parallel, people are working on computation and trying to understand computation, right?

394
00:25:01.428 --> 00:25:09.470
In the early decades of the digital revolution, where you've got these vacuum tubes and you're trying to understand, like, mathematical abstraction, computation is simply that.

395
00:25:09.550 --> 00:25:11.690
It's just a mathematical abstraction, okay?

396
00:25:11.970 --> 00:25:14.631
It's divorced from, like, physical substrates.

397
00:25:19.272 --> 00:25:23.197
is the same as entropy, but it's still this mathematical abstraction, okay?

398
00:25:24.318 --> 00:25:31.427
Rolf Landauer, he's actually at IBM Research, which we might hear a lot more about in this episode and in the next episode.

399
00:25:32.087 --> 00:25:32.928
More on that later.

400
00:25:33.269 --> 00:25:35.752
But Rolf Landauer, in 1961...

401
00:25:37.687 --> 00:25:42.030
he establishes that information is actually inherently physical.

402
00:25:42.471 --> 00:25:53.780
And he demonstrates this by saying that any logically irreversible operation, meaning something that destroys information, is going to cost you heat.

403
00:25:54.933 --> 00:25:56.314
Okay, here's what I mean by that.

404
00:25:56.394 --> 00:26:04.119
Like, there's a fundamental minimum amount of thermal energy that needs to be dissipated into an environment.

405
00:26:04.939 --> 00:26:08.682
And the amount of energy for erasing a bit, and I'll tell you what that means.

406
00:26:08.702 --> 00:26:10.183
Like, what does erasing a bit mean?

407
00:26:10.463 --> 00:26:20.909
But in any case, the fundamental amount of energy that you need to erase a bit and to let go of that heat is the temperature multiplied by Boltzmann constant multiplied by log of two.

408
00:26:21.189 --> 00:26:23.411
The KBT is like the amount of jiggle that you have

409
00:26:23.871 --> 00:26:26.573
for everything that can jiggle, every degree of freedom.

410
00:26:26.673 --> 00:26:32.758
And the log 2 is like, it reminds you of like entropy is the log of the number of microstates.

411
00:26:32.839 --> 00:26:37.002
In this case, the number of microstates is 2 because it's a 0 or a 1.

412
00:26:37.222 --> 00:26:39.024
So that's the amount of heat that you have to put out.

413
00:26:39.144 --> 00:26:44.208
Now, for normal computers, that's fine because we actually use reversible gates in our logic all the time.

414
00:26:44.248 --> 00:26:47.291
Our computers, the algorithms in our phones, everything uses...

415
00:26:48.407 --> 00:26:50.468
like AND gates, OR gates, things like that.

416
00:26:50.508 --> 00:26:55.330
If we just look at an AND gate, for example, let me show you how this thing erases information.

417
00:26:55.851 --> 00:26:57.712
An AND gate takes your inputs.

418
00:26:57.752 --> 00:26:59.973
There's two inputs that are either 0 or 1.

419
00:27:00.073 --> 00:27:04.495
And only if they're both 1 does the output become 1.

420
00:27:04.795 --> 00:27:09.297
Now, what that means is there's four different possibilities, 0, 0, 0, 1, 1, 0, 1, 1.

421
00:27:09.858 --> 00:27:11.359
But they get mapped to only 2.

422
00:27:12.539 --> 00:27:16.301
The first three get mapped to zero because at least one of them is zero.

423
00:27:16.581 --> 00:27:18.962
And only the last one, the 1, 1, gets mapped to a 1.

424
00:27:19.563 --> 00:27:28.787
Now, this is irreversible because if I were to give you the output, the table in C, you could not tell me the input, the A and B, right?

425
00:27:28.827 --> 00:27:30.288
Because there's redundancy.

426
00:27:30.388 --> 00:27:33.970
Like if I gave you the output as 1, then of course you could tell me it's 1, 1.

427
00:27:34.570 --> 00:27:38.211
But if the output is zero, then you couldn't tell me which of the three it came from.

428
00:27:38.811 --> 00:27:42.212
So that's an erasure of information because you lost a bit of information.

429
00:27:42.252 --> 00:27:43.292
Before you had two bits.

430
00:27:43.712 --> 00:27:44.833
Now you've only got one bit.

431
00:27:45.313 --> 00:27:45.553
Okay?

432
00:27:45.853 --> 00:27:49.494
So whenever you implement an AND gate, Landauer's principle comes in.

433
00:27:50.374 --> 00:27:52.595
And you're going to have to release some amount of heat.

434
00:27:53.915 --> 00:27:57.196
And the ability to go back is what's being released in the heat.

435
00:27:57.256 --> 00:27:57.496
Yes.

436
00:27:57.516 --> 00:28:01.117
The degradation of understanding what your previous state was.

437
00:28:01.157 --> 00:28:01.857
Exactly.

438
00:28:01.897 --> 00:28:04.678
It's kind of like an arrow of time argument that you're making.

439
00:28:04.718 --> 00:28:06.799
The TVA from Loki season one.

440
00:28:07.079 --> 00:28:07.279
Yeah.

441
00:28:07.699 --> 00:28:10.600
And this is totally okay for classical computing.

442
00:28:10.620 --> 00:28:14.161
We use so many N gates and OR gates in our... Fine.

443
00:28:15.902 --> 00:28:17.182
In our classical laptops, right?

444
00:28:17.202 --> 00:28:17.582
Fine.

445
00:28:17.682 --> 00:28:19.843
In quantum mechanics, this is not okay.

446
00:28:20.284 --> 00:28:20.544
Okay?

447
00:28:20.584 --> 00:28:21.384
There's two reasons.

448
00:28:21.804 --> 00:28:23.385
The first one is kind of simple, right?

449
00:28:23.425 --> 00:28:32.629
If we want to use quantum mechanics to do computation, we want to work with the quantum magic that happens with the entangling, that stuff that I was talking about with Bell's theorem.

450
00:28:32.669 --> 00:28:34.971
And, like, you know, these two states are entangled.

451
00:28:35.331 --> 00:28:39.433
Now, in order to keep the quantum state sort of happy...

452
00:28:40.423 --> 00:28:41.463
You better not heat it up.

453
00:28:42.044 --> 00:28:44.725
You better not let random other crap go in.

454
00:28:45.245 --> 00:28:51.748
But if you're dissipating heat in the middle of your computation, that is going to destroy all of the quantum mechanics of your system.

455
00:28:52.208 --> 00:28:52.448
Right?

456
00:28:53.228 --> 00:28:58.911
Because your quantum system almost has to maintain this single Lego block state.

457
00:28:59.851 --> 00:29:01.352
And it can't be messed around with.

458
00:29:02.192 --> 00:29:06.636
Because then that fundamentally changes the quantum magic of the system.

459
00:29:06.696 --> 00:29:07.377
Exactly, yeah.

460
00:29:07.437 --> 00:29:19.928
It's like the only part, and this is the next fundamental thing, the only part of quantum mechanics that is irreversible, meaning you can't go backwards, is the opening of the box or the measurement, the observation.

461
00:29:19.948 --> 00:29:20.769
The observation.

462
00:29:20.809 --> 00:29:21.009
Right?

463
00:29:21.049 --> 00:29:23.331
The observation is the thing where you can't go back.

464
00:29:23.872 --> 00:29:24.832
Before observing...

465
00:29:25.593 --> 00:29:31.399
Quantum mechanics is like kind of deterministic because Schrodinger's equation just like tells you how the quantum states are going to evolve.

466
00:29:31.719 --> 00:29:36.524
It's only when you open the box and find out if the cat is dead or alive, is the cat dead or alive.

467
00:29:36.644 --> 00:29:43.811
Otherwise, there's like, you know, states where the cat is dead and the cat is alive and there's a complex amplitude that is attached to both and they both...

468
00:29:44.992 --> 00:29:47.394
go forward like Schrodinger's equations.

469
00:29:47.834 --> 00:29:50.736
This means that quantum mechanics has unitary evolution.

470
00:29:51.236 --> 00:29:58.300
And so if I want to do computation with quantum mechanics, I cannot have reversible logic.

471
00:29:59.398 --> 00:30:00.258
which is kind of key.

472
00:30:00.919 --> 00:30:01.219
Okay.

473
00:30:01.279 --> 00:30:02.980
You cannot have reversible logic.

474
00:30:03.020 --> 00:30:03.260
Yeah.

475
00:30:03.300 --> 00:30:04.661
Wait, did I say that right?

476
00:30:04.921 --> 00:30:07.402
No, you can only have reversible logic.

477
00:30:07.463 --> 00:30:07.663
Yeah.

478
00:30:07.703 --> 00:30:08.323
Good, good, good.

479
00:30:08.343 --> 00:30:08.623
Yes.

480
00:30:08.643 --> 00:30:08.903
Right.

481
00:30:09.083 --> 00:30:18.909
Because the point is the system has to basically continuously maintain like, like basically until the point of observation, which you want to be able to decide when that happens.

482
00:30:18.969 --> 00:30:19.189
Yeah.

483
00:30:19.429 --> 00:30:26.613
You want to just be able to have this system operate in this state, which means it needs to be able to traverse between.

484
00:30:26.913 --> 00:30:27.134
Yeah.

485
00:30:28.054 --> 00:30:50.865
all of the quantum yeah and i need to be able to save like all of my progress in some sense okay no okay yeah i i i get the point that you're saying which is like the benefit of a quantum system is that um you don't mess with it until the end right everything is reversible yeah yeah like that you know yeah all of the quantum magic stays quantum magic and you're like messing with the quantum magic but now you have to do it in a

486
00:30:51.905 --> 00:31:10.118
irreversible way right right you have to obey the laws of schrodinger's equations and like unitary dynamics yes and like poke it in a very specific way that you're not like destroying the thing that is giving you all the magic we have a little poached egg we don't want to poke the yolk yes while it's cooking yeah

487
00:31:10.518 --> 00:31:10.718
Right.

488
00:31:10.758 --> 00:31:14.919
And then ruin our poached egg or souffle or any other kind of cooking analogy.

489
00:31:15.920 --> 00:31:33.184
I think that's a really interesting point, though, because now we're sort of helping to define the fundamentals differences between a classical and quantum systems such that we are going to build to this reason of why quantum systems give us these interesting other things we can do.

490
00:31:33.264 --> 00:31:33.464
Yeah.

491
00:31:33.864 --> 00:31:38.426
That fundamentally, because classical systems are irreversible.

492
00:31:38.746 --> 00:31:38.986
Mm hmm.

493
00:31:39.686 --> 00:31:46.752
You cannot get out of a classical system no matter how much power, compute, how well you dissipate the heat.

494
00:31:46.832 --> 00:31:47.352
None of that matters.

495
00:31:47.372 --> 00:31:48.693
Yeah, none of that matters.

496
00:31:48.773 --> 00:31:54.678
In order to work with the quantum magic, you got to work in the constraints of quantum mechanics and Schrodinger's equations.

497
00:31:54.698 --> 00:31:55.238
Very interesting.

498
00:31:55.258 --> 00:31:56.979
Or Heisenberg if you're in that camp, right?

499
00:31:57.280 --> 00:32:00.342
So it's unclear whether this is even possible, though.

500
00:32:00.742 --> 00:32:00.902
Right.

501
00:32:00.922 --> 00:32:06.587
Like, can you compute with reversible logic?

502
00:32:06.607 --> 00:32:07.107
Right.

503
00:32:07.418 --> 00:32:07.618
Right?

504
00:32:07.638 --> 00:32:10.180
Because we're used to AND gates and OR gates.

505
00:32:10.500 --> 00:32:15.603
And we got algorithms galore for days for that kind of stuff, right?

506
00:32:15.643 --> 00:32:21.087
1973, Charles Bennett demonstrates that you can actually use universal reversible computation.

507
00:32:22.367 --> 00:32:32.874
And along with him, Edward Fredkin and Tommaso Toffoli, who's over here, Tommaso Toffoli invents something called a Toffoli gate, which is a controlled-controlled-not gate.

508
00:32:34.154 --> 00:32:42.556
I don't want to get into all of that, but it's effectively a logic gate that is reversible, meaning I can always go backwards.

509
00:32:43.056 --> 00:32:49.617
The truth table is unique because my three inputs give me three outputs.

510
00:32:49.797 --> 00:32:53.118
So from those three outputs, I can always reconstruct my three inputs.

511
00:32:53.758 --> 00:32:58.419
But crucially, this gate is something that I can use for universal computation.

512
00:32:58.759 --> 00:33:00.800
I can build any other gate from these gates.

513
00:33:03.832 --> 00:33:04.512
It's possible.

514
00:33:04.592 --> 00:33:06.193
There's a chance.

515
00:33:06.253 --> 00:33:06.874
This makes sense.

516
00:33:06.954 --> 00:33:12.517
Unlike our previous AND gate, where three out of the four outputs, you could not go back from.

517
00:33:12.557 --> 00:33:14.298
Because it went two to one, right?

518
00:33:14.418 --> 00:33:15.859
So it's like, yeah, you lost some.

519
00:33:16.059 --> 00:33:16.960
Here, it's three to three.

520
00:33:17.000 --> 00:33:17.540
Three to three.

521
00:33:17.580 --> 00:33:20.842
So you basically retain all the degrees of information necessary.

522
00:33:20.862 --> 00:33:20.942
Yes.

523
00:33:21.222 --> 00:33:42.910
to go backwards um and that's a fundamental building block to now be able to potentially do the type of computation that you would you have uh the an enabling layer to potentially now think about the idea of quantum computing yes uh yes you've got like a substrate that i can start building an algorithm maybe maybe right maybe maybe

524
00:33:43.230 --> 00:33:51.261
And Toffoli, for those that are well-versed in quantum computing or just starting to learn about it, you'll hear a lot about Toffoli gates.

525
00:33:51.842 --> 00:33:54.325
That's who it's named after, right?

526
00:33:54.345 --> 00:33:59.292
And it's because it's this first idea of a gate that can make up universal...

527
00:34:00.734 --> 00:34:01.735
logic in some sense.

528
00:34:01.915 --> 00:34:09.721
So following this, Paul Benioff at the Argonne National Lab, he creates a quantum mechanics version of the state transitions in Turing machines.

529
00:34:09.821 --> 00:34:27.175
Alan Turing and Church, who we talked about again on our America 250, I keep pitching this thing, but they demonstrated at Princeton that any computable algorithm can be computed on a Turing machine using these state transitions and very simple logic

530
00:34:28.342 --> 00:34:31.866
He showed that, you know, there's a version of that that I can do in quantum mechanics, okay?

531
00:34:32.266 --> 00:34:40.836
Side note, Charles Bennett, who's the guy who demonstrated that first reversible computation, he was involved in the early days of quantum cryptography.

532
00:34:41.396 --> 00:34:44.880
So his undergrad friend, Stephen Wissner, at...

533
00:34:46.330 --> 00:34:52.132
at Columbia, they had an idea to use Heisenberg's uncertainty principle to create unforgeable money.

534
00:34:52.652 --> 00:34:57.193
So this is before Bitcoin was a thing before the blockchain was a thing.

535
00:34:57.493 --> 00:35:01.334
They were trying to use quantum mechanics to create money that you couldn't fake.

536
00:35:01.815 --> 00:35:02.675
Right.

537
00:35:02.735 --> 00:35:08.557
There's a funny story where Bennett attended the IEEE conference on foundations of computer science in Puerto Rico.

538
00:35:09.277 --> 00:35:13.078
And on one of these afternoons, this cryptographer,

539
00:35:13.921 --> 00:35:15.223
Jill is brassard.

540
00:35:15.623 --> 00:35:19.188
He was swimming out in the beachfront hotel in San Juan and he,

541
00:35:20.195 --> 00:35:27.919
Bennett just swims up to him in the ocean and just starts ranting at him about this idea of quantum money.

542
00:35:29.019 --> 00:35:33.362
And the quote we have from Brassard is, like, I was trapped, so I listened politely.

543
00:35:33.422 --> 00:35:35.002
Because they're in the middle of the ocean.

544
00:35:35.022 --> 00:35:39.224
Brassard's just trying to have a good time before his talk about cryptography.

545
00:35:39.244 --> 00:35:41.726
In Puerto Rico, he's not trying to have a good time.

546
00:35:41.766 --> 00:35:45.328
Yeah, he's trying to have a good time, and Bennett just swims up to him and is like, yo.

547
00:35:46.757 --> 00:35:48.058
Quantum money.

548
00:35:48.138 --> 00:35:49.059
I got this idea.

549
00:35:49.079 --> 00:35:49.939
I got this idea.

550
00:35:49.959 --> 00:35:51.140
It's going to make us rich.

551
00:35:51.540 --> 00:35:52.001
Probably.

552
00:35:52.021 --> 00:35:52.921
I don't know what he said, right?

553
00:35:53.222 --> 00:35:57.825
But soon as he's listening to this thing, it's like doubt turns into fascination.

554
00:35:57.925 --> 00:36:01.588
And he realizes, like, this could actually be some serious science.

555
00:36:02.208 --> 00:36:04.590
And the two of them form a collaboration together.

556
00:36:04.870 --> 00:36:08.353
that starts a whole new field of quantum information science.

557
00:36:08.914 --> 00:36:10.515
They win the Turing Prize together.

558
00:36:11.556 --> 00:36:18.261
And there's this discovery of a fundamental connection between physics and information, quantum teleportation, if you've ever heard of.

559
00:36:18.662 --> 00:36:19.442
That's these guys.

560
00:36:19.563 --> 00:36:29.951
So they won the Turing Prize together, but all from a serendipitous meeting in Puerto Rico, in the ocean, right, where Bennett just like...

561
00:36:30.752 --> 00:36:45.557
accosted this guy this the only context i have recently of this idea of quantum teleportation was a news story maybe from a year or two ago where the the chinese apparently were able to that they had the maximum distance from

562
00:36:46.157 --> 00:37:14.074
of quantum teleportation of information they had like a satellite oh dude i heard about that something on the ground and when i heard that i'm in because like the idea is like it is you cannot hack that information transfer yeah in the way you would with normal signals intelligence yeah that's like getting into quantum cryptography and stuff like that again this is the stuff that these guys are doing wait so yeah it starts here on a beach in puerto rico yeah yeah and now it's in orbit yeah but that's it we're gonna get there i think in terms of being able to better understand yeah

563
00:37:14.634 --> 00:37:15.456
what that means.

564
00:37:15.536 --> 00:37:21.507
But this is what we talk about when we say that there are all these stories and headlines and tech blogs and whatever.

565
00:37:21.527 --> 00:37:21.968
Oh, yeah.

566
00:37:22.930 --> 00:37:26.353
Quantum teleportation, everything is going to be whatever.

567
00:37:26.513 --> 00:37:30.497
Yeah, but it starts with these small meetings between human beings, right?

568
00:37:30.577 --> 00:37:32.159
At conferences, crucially.

569
00:37:32.199 --> 00:37:32.399
Yes.

570
00:37:32.499 --> 00:37:37.624
So when people say that they don't want to fund conferences, conferences is where ideas come together.

571
00:37:37.724 --> 00:37:38.204
Osmosis.

572
00:37:38.224 --> 00:37:41.447
You know, like it's very important to bring human beings together.

573
00:37:42.688 --> 00:37:45.230
So this is the status in the early 1980s, okay?

574
00:37:45.511 --> 00:37:48.974
We've got some indication that quantum computing could work.

575
00:37:49.294 --> 00:37:49.514
Right?

576
00:37:49.594 --> 00:37:52.055
Like Landau's principle is not a no-go that we thought.

577
00:37:52.435 --> 00:37:55.497
There's ways to get around heat dissipation.

578
00:37:55.837 --> 00:38:05.441
There's also this fundamental advantage that Bell gives you with quantum mechanics, where he says that quantum mechanics is certainly very different from classical mechanics.

579
00:38:05.481 --> 00:38:05.681
Right?

580
00:38:05.981 --> 00:38:07.282
And there is some magic there.

581
00:38:07.982 --> 00:38:10.823
Feynman comes in over here.

582
00:38:11.083 --> 00:38:11.344
Okay?

583
00:38:11.664 --> 00:38:13.244
So this is where Feynman enters the fray.

584
00:38:13.925 --> 00:38:14.225
Okay.

585
00:38:15.215 --> 00:38:18.197
He visits his old alma mater, MIT.

586
00:38:18.857 --> 00:38:21.179
We make fun of MIT a lot on this podcast.

587
00:38:22.099 --> 00:38:24.721
In this one, I'll have to give him credit.

588
00:38:24.861 --> 00:38:32.426
MIT and IBM, in May 1981, they sponsored the Physics of Computation Conference at MIT's Endicott House.

589
00:38:32.806 --> 00:38:34.427
It's kind of like their Camp David show.

590
00:38:35.324 --> 00:38:36.385
for like conferences.

591
00:38:36.446 --> 00:38:43.935
It's like out in the outskirts of Boston, surrounded by the woods, this old, old like mansion out in the woods.

592
00:38:44.336 --> 00:38:50.323
Princeton has something similar, like with Prospect House, you know, in the middle of, but ours is on campus, in the middle of campus.

593
00:38:50.704 --> 00:38:52.706
UCLA has something that's similar.

594
00:38:53.467 --> 00:38:54.990
out in Lake Arrowhead, actually.

595
00:38:55.711 --> 00:38:56.492
That's nice.

596
00:38:56.552 --> 00:38:59.436
I had the pleasure of attending like a neuroscience workshop there.

597
00:38:59.476 --> 00:39:00.317
It's really nice.

598
00:39:00.337 --> 00:39:00.778
That's really nice.

599
00:39:00.798 --> 00:39:06.186
So, you know, universities have these like retreats and MIT sponsored this at Endicott House.

600
00:39:06.266 --> 00:39:08.770
And this conference was attended by a who's who.

601
00:39:09.791 --> 00:39:12.333
of quantum computing people, or just computing people in general.

602
00:39:12.693 --> 00:39:19.779
This is a photo that was taken by Charles Bennett, the guy who went into the ocean and tried to pitch this quantum money thing.

603
00:39:20.019 --> 00:39:21.160
So Charles Bennett was there.

604
00:39:22.801 --> 00:39:28.846
Along with, you've got Freeman Dyson on the left, Paul Benioff, Paul Benioff's the Turing machine guy.

605
00:39:28.986 --> 00:39:33.330
You've got Rolf Landauer, that's the Landauer limit thing.

606
00:39:33.630 --> 00:39:35.171
John Wheeler, Wheeler's just there.

607
00:39:35.572 --> 00:39:36.432
Wheeler's everywhere.

608
00:39:37.413 --> 00:39:37.673
Yeah.

609
00:39:37.874 --> 00:39:39.595
He's like a Nick Fury in Marvel.

610
00:39:39.675 --> 00:39:40.476
Yeah, dude.

611
00:39:40.556 --> 00:39:41.137
Oh, my God.

612
00:39:41.177 --> 00:39:42.979
That's such a good analogy.

613
00:39:43.720 --> 00:39:43.960
Yeah.

614
00:39:44.020 --> 00:39:46.803
Wheeler is the Nick Fury of 20th century physics.

615
00:39:47.183 --> 00:39:47.404
Yeah.

616
00:39:47.604 --> 00:39:51.648
And then, of course, Richard Feynman and Tom Toffoli.

617
00:39:52.423 --> 00:39:56.204
So all of the guys that we just talked about, they're at this conference, right?

618
00:39:56.664 --> 00:39:58.365
Feynman gives the keynote address.

619
00:39:58.605 --> 00:40:00.946
It's titled Simulating Physics with Computers.

620
00:40:01.366 --> 00:40:04.707
It's published in 1982 in the International Journal of Theoretical Physics.

621
00:40:05.107 --> 00:40:06.487
This is the paper that came out of it.

622
00:40:07.368 --> 00:40:14.170
And this is where he reframes quantum properties from the computational obstacles into fundamental assets.

623
00:40:15.030 --> 00:40:15.990
And here's what I mean by that.

624
00:40:16.210 --> 00:40:18.531
Prior to this talk,

625
00:40:20.050 --> 00:40:22.111
Everyone thought of quantum mechanics as a nuisance.

626
00:40:22.872 --> 00:40:27.714
Because when you're trying to make semiconductors into chips, quantum mechanics is a nuisance.

627
00:40:28.134 --> 00:40:29.975
Stuff is moving around, right?

628
00:40:30.015 --> 00:40:32.357
There's like, you got to worry about the band structure.

629
00:40:32.377 --> 00:40:36.939
But if your growth is not great, then the electrons are going to hop everywhere.

630
00:40:37.239 --> 00:40:38.500
There's all sorts of noise.

631
00:40:38.820 --> 00:40:41.601
And quantum mechanics is primarily that source of noise, right?

632
00:40:41.862 --> 00:40:44.403
You got quantum tunneling, the thermal fluctuations.

633
00:40:45.323 --> 00:40:48.005
It limits how small you can make your transistors, things like that.

634
00:40:48.485 --> 00:40:50.286
Feynman inverted this perspective.

635
00:40:51.007 --> 00:41:02.594
And he analyzed, what if you could create computational complexity by simulating quantum mechanics using a quantum computer, a computer that uses quantum mechanics?

636
00:41:03.194 --> 00:41:04.455
Now, why would we want to do that?

637
00:41:04.815 --> 00:41:09.378
Well, literally, reality is an interacting quantum system system.

638
00:41:09.784 --> 00:41:10.764
of particles, right?

639
00:41:10.824 --> 00:41:13.565
Like quantum mechanics is the reality.

640
00:41:14.246 --> 00:41:24.169
And even if you talk about the 10 to the 80 atoms in the universe or like water having the 10 interacting electrons, it's still quantum mechanical.

641
00:41:24.209 --> 00:41:25.249
So it certainly makes sense.

642
00:41:25.890 --> 00:41:27.410
So here's what Feynman said.

643
00:41:27.450 --> 00:41:31.772
He said, suppose I want to simulate the physics of these interacting particles, right?

644
00:41:32.332 --> 00:41:35.593
How much stuff would I need to store in my classical computer?

645
00:41:36.268 --> 00:41:36.548
Mm-hmm.

646
00:41:37.029 --> 00:41:38.371
This is where Bell's theorem came in.

647
00:41:38.411 --> 00:41:38.711
Mm-hmm.

648
00:41:39.011 --> 00:41:39.272
Okay?

649
00:41:39.452 --> 00:41:39.712
Mm-hmm.

650
00:41:40.193 --> 00:41:49.284
Remember, I was harping on earlier this idea that the physics of two particles cannot be factored into two independent mathematical probabilities.

651
00:41:49.384 --> 00:41:51.026
We have to look at it as one Lego block.

652
00:41:51.066 --> 00:41:51.186
Yes.

653
00:41:51.226 --> 00:41:54.170
Not two smaller Lego blocks that make up this bigger Lego block.

654
00:41:54.190 --> 00:41:54.610
Yeah, yeah.

655
00:41:54.650 --> 00:42:01.095
You can't say that this is what the stuff on the left with Alice is doing and this is what the stuff on the right with Bob is doing, right?

656
00:42:01.196 --> 00:42:04.978
Instead, there's no way to combine them later on, right?

657
00:42:05.819 --> 00:42:09.242
If you could, then simulating an n-particle quantum system…

658
00:42:10.302 --> 00:42:12.384
where the classical computer would be pretty straightforward.

659
00:42:12.404 --> 00:42:19.752
You just create some kind of software program that assigns like N independent data tables or subroutines for all of the N independent particles.

660
00:42:20.072 --> 00:42:20.833
You look them up.

661
00:42:20.993 --> 00:42:23.616
Each is tracking some kind of isolated local state.

662
00:42:24.056 --> 00:42:30.783
And then your memory and processing time scales linearly, like the order of N, like however many particles you have, that's about...

663
00:42:31.406 --> 00:42:32.287
how it's going to scale.

664
00:42:32.667 --> 00:42:35.369
The point being, it just becomes a compute and power.

665
00:42:35.469 --> 00:42:39.672
Yeah, and you just make a bigger computer, and it's fine.

666
00:42:39.692 --> 00:42:46.376
You could scale up to some upper bound that then covers all the types of simulations you're trying to do.

667
00:42:46.396 --> 00:42:49.799
And you just have one subroutine for each particle, and you're fine.

668
00:42:49.839 --> 00:42:50.299
And you're fine.

669
00:42:50.339 --> 00:42:50.519
Right?

670
00:42:51.019 --> 00:42:54.242
But quantum probability distributions do not factor.

671
00:42:54.782 --> 00:42:55.682
That's what Bell showed.

672
00:42:55.803 --> 00:42:56.023
Right.

673
00:42:56.103 --> 00:42:56.303
Right?

674
00:42:56.823 --> 00:42:59.225
If you want to talk about reality...

675
00:43:00.461 --> 00:43:01.962
The experiments show this, right?

676
00:43:01.983 --> 00:43:04.505
This is no longer in our head, right?

677
00:43:04.825 --> 00:43:10.631
For an n-particle system, you can't decompose it into n different things.

678
00:43:11.412 --> 00:43:14.795
Instead, you have to worry about all of them combined.

679
00:43:14.835 --> 00:43:17.998
It depends globally on the fully entangled configuration of

680
00:43:18.627 --> 00:43:20.508
of your particles, right?

681
00:43:20.948 --> 00:43:25.609
So even if you imagine like a two-state particle, like the one that we talked about with Alice and Bob, right?

682
00:43:25.669 --> 00:43:30.070
You've got a two-state particle of spins that can be like, you know, spin up or spin down.

683
00:43:32.751 --> 00:43:44.695
A classical computer would be forced to store and update a joint probability, like vector, tensor, or like set of numbers to...

684
00:43:45.648 --> 00:43:49.312
Across all two to the n computational states.

685
00:43:49.672 --> 00:43:51.353
For Alice and Bob, for example, right?

686
00:43:52.675 --> 00:43:53.976
You could have up, up.

687
00:43:54.476 --> 00:43:55.397
You could have down, down.

688
00:43:55.738 --> 00:43:57.399
You could have up, down, or down, up.

689
00:43:58.000 --> 00:43:58.901
And those are different.

690
00:43:59.201 --> 00:44:00.962
Across both the z and the x?

691
00:44:01.603 --> 00:44:03.505
Well, here I'm just saying like...

692
00:44:03.545 --> 00:44:05.987
Even if you keep it that simple.

693
00:44:06.107 --> 00:44:08.029
Yeah, even if we just keep it that simple, right?

694
00:44:08.049 --> 00:44:08.169
Okay.

695
00:44:09.090 --> 00:44:09.270
Right.

696
00:44:09.450 --> 00:44:12.493
Which, like, the point being it's not... Yeah.

697
00:44:12.754 --> 00:44:13.014
Anyway.

698
00:44:13.234 --> 00:44:17.138
Yeah, the Z and the X comes in, like, a bit later, and I'll have to get in, you know... Let's not go there.

699
00:44:17.158 --> 00:44:19.380
Because, like, they're all, like, yeah, whatever.

700
00:44:19.800 --> 00:44:22.743
In any case, like, let's just say two particle states, right?

701
00:44:22.763 --> 00:44:23.004
Okay.

702
00:44:23.024 --> 00:44:24.004
Two state systems, right?

703
00:44:24.044 --> 00:44:25.386
Those two states can actually go...

704
00:44:25.746 --> 00:44:46.159
in z and x is the point that i was trying to make but but um what you need to do is for alice and bob you need to keep track of four possibilities the up up the down down the down up and the and the and the up down really you got to take take um take care of like the sum of this and the difference of this because like you know what does it mean to be like the the the

705
00:44:46.519 --> 00:44:49.122
Electron 1 is up and electron 2 is down.

706
00:44:49.142 --> 00:44:52.266
There's no sticker on an electron saying this is 1 and 2.

707
00:44:52.306 --> 00:44:53.708
They're indistinguishable particles.

708
00:44:53.728 --> 00:44:57.713
So you have to worry about, like, you know, combining linear combinations of them.

709
00:44:57.953 --> 00:45:01.257
But in any case, it's always 2 to the n is the idea.

710
00:45:01.577 --> 00:45:01.797
Now...

711
00:45:02.458 --> 00:45:05.579
This becomes insurmountable very, very quickly.

712
00:45:05.979 --> 00:45:06.860
Very, very quickly.

713
00:45:06.940 --> 00:45:14.722
Okay, if you want 50 entangled two-state particles, that's 2 to the 50 complex numbers that you have to take care of, right?

714
00:45:15.022 --> 00:45:18.523
2 to the 50, hack for students that are listening.

715
00:45:19.264 --> 00:45:23.645
2 to the 10 is like 10 to the 3 because 2 to the 10 is 1024, which is 10 to the 3.

716
00:45:23.925 --> 00:45:25.746
So if you ever want to go into base 10...

717
00:45:26.246 --> 00:45:30.130
2 to the 50 is like 10 to the 3 to the 5, which is 10 to the 15.

718
00:45:30.150 --> 00:45:32.332
So you got to take care of 10 to the 15 complex numbers.

719
00:45:32.653 --> 00:45:36.977
If you're trying to simulate 300 two-state particles, which like any...

720
00:45:37.237 --> 00:45:41.762
There's so many compounds where there's 300 electrons that are moving around, proteins, for example.

721
00:45:43.103 --> 00:45:44.565
That's going to be 2 to the 300, which is...

722
00:45:47.587 --> 00:45:53.328
2 to the 10 to the 30, which is 10 to the 3 to the 30, which is 10 to the 90 numbers.

723
00:45:54.009 --> 00:45:58.189
That exceeds the number of elementary particles in our observable universe.

724
00:45:58.229 --> 00:46:01.910
There's estimates out there that there are only 10 to the 80 atoms, right?

725
00:46:02.150 --> 00:46:08.992
So just to simulate 300 two-state particles, I need 10 to the 90 numbers, right?

726
00:46:10.738 --> 00:46:11.939
It's kind of crazy.

727
00:46:12.500 --> 00:46:22.908
Part of the point you're bringing up here is that it is just wholly inefficient because the type of systems we would be able to simulate are exceedingly small, effectively a protein.

728
00:46:23.229 --> 00:46:23.429
Yeah.

729
00:46:23.509 --> 00:46:25.991
That only had two states, which is not real.

730
00:46:26.191 --> 00:46:26.311
Yeah.

731
00:46:26.371 --> 00:46:28.053
It's not practical in real life.

732
00:46:28.073 --> 00:46:28.253
Yeah.

733
00:46:28.293 --> 00:46:28.473
Yeah.

734
00:46:28.733 --> 00:46:30.916
No, I'm saying a protein would be crazy.

735
00:46:30.956 --> 00:46:38.703
I mean, maybe you could simulate, if you had all the time in the universe, like a water molecule with 10 electrons, right?

736
00:46:38.783 --> 00:46:53.197
There's no amount of brute force around compute and scaling up that would make it even tenable because the amount of variables when we have to account for the entire system as a whole...

737
00:46:54.969 --> 00:46:56.791
Because you can't factor it.

738
00:46:57.231 --> 00:47:08.441
It means that the amount of variables and interactions you're tracking continuously is just insane.

739
00:47:08.481 --> 00:47:17.729
It's just... Yeah, and also as an aside, I think it's kind of cool to think about that somehow the universe is keeping track of what?

740
00:47:17.789 --> 00:47:18.690
So there's 10 to the 80...

741
00:47:19.233 --> 00:47:19.934
particles, right?

742
00:47:20.054 --> 00:47:29.022
Even if all those particles are two-state systems, there's two to the 10 to the 80 complex amplitudes that the universe is keeping track.

743
00:47:29.082 --> 00:47:31.644
I don't even know how big that number is, right?

744
00:47:31.764 --> 00:47:38.310
That might be, I don't know if that's the big, no, I'm sure there's mathematicians that have come up with bigger numbers than two to the 10 to the 80.

745
00:47:38.790 --> 00:47:42.033
But I'm just saying, like, it's kind of crazy that the universe is keeping track of

746
00:47:42.634 --> 00:47:45.898
all of those complex amplitudes to give us the world.

747
00:47:46.038 --> 00:47:47.380
Is that how it works, really?

748
00:47:47.881 --> 00:47:49.022
Is that really how it works?

749
00:47:49.343 --> 00:47:53.468
Sometimes I'm thinking about this stuff, and I'm like, mate, is this really how it works?

750
00:47:54.229 --> 00:47:55.471
Because it's hard to even...

751
00:47:56.694 --> 00:48:02.115
And like where anyway, yeah, but that's, that's an aside about like, just like the nature of reality.

752
00:48:02.195 --> 00:48:03.215
Totally, totally, totally.

753
00:48:03.355 --> 00:48:04.736
Why quantum mechanics is weird.

754
00:48:04.756 --> 00:48:07.216
But in any case, right, this is what Feynman is talking about.

755
00:48:07.256 --> 00:48:16.978
And he says, instead of classical bits where we'd have to, we'd have to create 10 to the 90 bits to keep track of 300 thingies.

756
00:48:18.858 --> 00:48:21.979
Instead, what if we use a quantum version of a bit, right?

757
00:48:22.039 --> 00:48:23.319
What if we create a computer and,

758
00:48:24.596 --> 00:48:27.097
Where the bit is a two-state quantum system.

759
00:48:27.937 --> 00:48:32.978
And then we bake into the computer the interaction that we're trying to study, right?

760
00:48:33.418 --> 00:48:44.421
Then the quantum mechanics inside the computer is going to take care of all of the superposition, entanglement, and all of the blow-up of complex numbers, right?

761
00:48:44.501 --> 00:48:47.762
Because we're just harnessing the quantum mechanics that we're trying to study.

762
00:48:48.422 --> 00:48:50.804
At the foundational layer of where the compute happens.

763
00:48:50.845 --> 00:48:51.685
Yeah, hardware is king.

764
00:48:52.086 --> 00:48:55.108
Versus after the fact at the software level or at the systems level.

765
00:48:55.188 --> 00:48:55.909
Yes, exactly.

766
00:48:55.969 --> 00:49:02.515
And so he ends his talk with a very famous line that rings across a lot of...

767
00:49:03.620 --> 00:49:07.462
quantum computing literature and a lot of quantum computing deep dives.

768
00:49:07.722 --> 00:49:09.823
He says, nature isn't classical, damn it.

769
00:49:10.303 --> 00:49:13.844
And if you want to take a simulation of nature, you'd better make it quantum mechanical.

770
00:49:13.864 --> 00:49:17.826
And by golly, it's a wonderful problem because it doesn't look so easy.

771
00:49:18.486 --> 00:49:20.767
No, it certainly doesn't.

772
00:49:21.027 --> 00:49:23.068
It certainly does not look so easy.

773
00:49:23.088 --> 00:49:26.950
46 years later, we're still trying to make one.

774
00:49:27.923 --> 00:49:43.176
I think this is a really great starting point because what we've done so far is we've sort of created this understanding of the difference between classical systems versus quantum mechanical systems at a theoretical level.

775
00:49:44.237 --> 00:49:50.362
How that informed the early countercultural era of computing in general.

776
00:49:51.223 --> 00:49:54.546
How this idea then moved to this point of computing.

777
00:49:55.166 --> 00:50:14.274
There is actually quantum computing as a competing way to solve certain types of problems as opposed to classical computing because there are fundamental limitations because we've found violations of Bell's theorem that mean that the hidden variable thing and the realists, sorry.

778
00:50:15.274 --> 00:50:21.257
And if we really want to create simulations that are true to our lived theory

779
00:50:21.995 --> 00:50:23.578
four dimensional time space.

780
00:50:23.598 --> 00:50:23.898
Yeah.

781
00:50:23.938 --> 00:50:24.339
Whatever.

782
00:50:24.499 --> 00:50:24.760
Yeah.

783
00:50:25.000 --> 00:50:25.280
Right.

784
00:50:25.481 --> 00:50:26.843
This magical thingy.

785
00:50:27.103 --> 00:50:27.223
Um,

786
00:50:28.653 --> 00:50:40.201
we're going to need the compute layer to reflect the same quantum mechanical attributes that our theoretical frameworks currently suggest exist.

787
00:50:40.421 --> 00:50:41.102
Yes, exactly.

788
00:50:41.142 --> 00:50:41.822
Is that a fair summary?

789
00:50:41.842 --> 00:50:42.723
That's exactly right.

790
00:50:42.843 --> 00:50:50.208
And that talk happened in 1981, and he mentions all of the priors that I've been talking about.

791
00:50:50.269 --> 00:50:51.429
He mentions Bell's theorem.

792
00:50:51.730 --> 00:50:54.752
He mentions Toffoli and Benioff and all these people who said –

793
00:50:55.232 --> 00:50:57.855
Hey, quantum computing is a possibility, right?

794
00:50:58.135 --> 00:51:00.158
We have reversible logic.

795
00:51:00.398 --> 00:51:00.578
Right.

796
00:51:00.798 --> 00:51:06.104
We have a paradigm where we can manipulate a quantum state, right, even theoretically.

797
00:51:06.625 --> 00:51:12.592
And Bell shows that there's this rich underlying layer that we can actually exploit if we want to, right?

798
00:51:12.692 --> 00:51:12.972
Mm-hmm.

799
00:51:14.033 --> 00:51:24.777
Feynman's argument about fundamental science and like, you know, this becomes something that is a polynomial time simulation tool for chemistry, condensed matter physics, material science, everything.

800
00:51:24.817 --> 00:51:29.539
But that's really not the reason why quantum computing is a trillion dollar industry.

801
00:51:29.999 --> 00:51:37.823
I don't think a trillion dollars would have gone into quantum computing if all it was doing was trying to find the next room temperature superconductor.

802
00:51:38.043 --> 00:51:38.243
Okay.

803
00:51:38.403 --> 00:51:38.684
Okay?

804
00:51:39.024 --> 00:51:46.328
The reason it is a trillion dollar computing industry is because of the stuff that we are getting into after our break.

805
00:51:46.608 --> 00:51:47.028
Namely…

806
00:51:48.685 --> 00:51:53.986
Shores algorithm and Bitcoin going to zero.

807
00:51:55.047 --> 00:51:57.207
And so with that, let's do some housekeeping.

808
00:51:57.727 --> 00:52:02.929
So for those of you watching us on YouTube or Spotify, welcome.

809
00:52:03.449 --> 00:52:09.671
As always, watching the pod is one of the best ways to capture all of the overlays and graphics we talk about.

810
00:52:10.071 --> 00:52:11.271
Be sure to like it.

811
00:52:11.651 --> 00:52:13.492
share, comment, and subscribe.

812
00:52:13.813 --> 00:52:17.636
It helps us in our battle against the billionaire algorithm.

813
00:52:17.936 --> 00:52:29.104
For those listening on Apple Podcasts, it is out of our hands, but we are awaiting the announcement for Spotify creator videos to be available as video on Apple Podcasts.

814
00:52:29.484 --> 00:52:37.871
Allegedly, Apple and Spotify are collaborating on this launching late 2026, so keep an eye out for that.

815
00:52:38.131 --> 00:52:39.572
For those who catch our clips today,

816
00:52:39.982 --> 00:52:42.243
on TikTok and Instagram on a regular basis.

817
00:52:42.924 --> 00:52:44.365
Put them in those group DMs.

818
00:52:44.845 --> 00:52:48.167
Share the best science show on the planet with your friends, coworkers.

819
00:52:48.227 --> 00:52:49.147
Bring it to Journal Club.

820
00:52:49.648 --> 00:52:54.771
If you are watching this full episode for the first time from our clips, welcome.

821
00:52:55.391 --> 00:52:56.592
Every episode is like this.

822
00:52:57.112 --> 00:53:00.634
And so we are super excited to continue to have you all today.

823
00:53:00.654 --> 00:53:05.016
A couple of announcements or housekeeping notes.

824
00:53:05.596 --> 00:53:13.039
For our merch giveaway, we are going to be sending out the emails to the winners over the next week here.

825
00:53:13.100 --> 00:53:15.060
So keep an eye out on your email.

826
00:53:15.341 --> 00:53:18.142
Thank you for everyone for submitting for our one-year anniversary.

827
00:53:18.502 --> 00:53:24.564
You may have noticed behind us there are gold balloons representing 250.

828
00:53:25.024 --> 00:53:32.966
And while we talked a lot about America 250, the gold balloons are not necessarily here to celebrate our America 250 episode.

829
00:53:33.006 --> 00:53:44.470
But they are here thanks to the loving wives, Anna and Joni, who have provided us a way to celebrate our 250 Instagram followers, which is already now at 267.

830
00:53:45.956 --> 00:53:48.377
So we are just growing unbelievably fast.

831
00:53:48.697 --> 00:53:56.020
We want to thank the upcoming cast of The Real Housewives of FFP for supporting us so greatly.

832
00:53:56.660 --> 00:53:58.180
We love you both so much.

833
00:53:58.841 --> 00:54:02.522
And I'm just going to hit one last note before we get here.

834
00:54:02.882 --> 00:54:08.486
into some quick headlines as a palate cleanser before we dive back into our quantum episodes.

835
00:54:08.786 --> 00:54:13.670
If you would like to support the show, five-star reviews, like, comment, share, subscribe.

836
00:54:13.970 --> 00:54:19.093
If you would like to donate to the show, you can head to ffppod.com backslash donate.

837
00:54:19.193 --> 00:54:20.814
Again, we are on all platforms.

838
00:54:21.335 --> 00:54:26.058
Our website has a great way to watch the videos, chapters, full transcripts.

839
00:54:26.478 --> 00:54:31.142
Links to all the research papers we talk about are all available there.

840
00:54:31.463 --> 00:54:43.393
But now we want to quickly just get into some of the top news stories from the week just to give you an idea of what's going on out there in the world of science.

841
00:54:43.513 --> 00:54:46.315
Our first story came out breaking today.

842
00:54:46.716 --> 00:54:52.521
It's been all over the news related to pharmaceutical giants Moderna and Merck saying, I

843
00:54:53.061 --> 00:55:08.011
today, Wednesday, which will be likely a day before you all watch this podcast, that an experimental vaccine treatment has shown signs of preventing cancer from returning or spreading in a study of high-risk melanoma patients.

844
00:55:08.092 --> 00:55:15.577
This was a combination of Moderna bringing their mRNA vaccine structure and Merck bringing their Keytruda.

845
00:55:16.077 --> 00:55:17.418
And the idea is they

846
00:55:17.818 --> 00:55:20.621
You know, we've talked about the immune system in the past on the pod.

847
00:55:21.041 --> 00:55:25.285
And part of the tough part about cancer cells is our immune system is not really able to identify them.

848
00:55:25.345 --> 00:55:25.565
Yeah.

849
00:55:25.605 --> 00:55:30.009
So it's like our police, our immune system is looking for the criminals and the criminals are kind of invisible.

850
00:55:30.490 --> 00:55:39.098
Apparently, the combination of these two things makes it able, the immune system able to identify what was previously not visible to them.

851
00:55:39.638 --> 00:55:50.729
However, they've not published their results in a peer-reviewed journal or released the new data, saying instead they will be presented at an upcoming medical meeting and shared with regulators.

852
00:55:51.069 --> 00:55:51.410
Oh, okay.

853
00:55:51.590 --> 00:55:53.292
However, there does seem to be –

854
00:55:54.853 --> 00:55:57.534
Some real – there does seem to be a there there.

855
00:55:57.654 --> 00:55:58.514
Okay.

856
00:55:59.014 --> 00:56:09.637
And so according to their news release, the mRNA-based vaccine was tested in a late-stage trial involving people who had had surgery to remove a melanoma, one of the deadliest forms of skin cancer.

857
00:56:09.937 --> 00:56:16.378
Apparently, this same methodology is also being applied to a few other types of cancer, and there's potential that it generalizes.

858
00:56:16.838 --> 00:56:17.378
Interesting.

859
00:56:17.598 --> 00:56:19.099
So their stock price –

860
00:56:19.939 --> 00:56:21.080
Both of them went through the roof.

861
00:56:21.320 --> 00:56:21.901
Oh, I bet.

862
00:56:22.101 --> 00:56:22.602
Around that.

863
00:56:22.682 --> 00:56:23.222
So we'll see.

864
00:56:23.242 --> 00:56:24.163
A cancer vaccine?

865
00:56:24.884 --> 00:56:25.364
The data.

866
00:56:25.544 --> 00:56:28.027
We'll see when the data comes in and we'll keep an eye on that.

867
00:56:28.047 --> 00:56:28.487
Sounds pretty good.

868
00:56:28.507 --> 00:56:31.670
But that's an interesting first story from us that's out today.

869
00:56:31.710 --> 00:56:35.674
Our second story in the news headlines that was interesting.

870
00:56:35.714 --> 00:56:38.797
This is from UC Berkeley.

871
00:56:38.837 --> 00:56:45.743
This idea of a new technique called trace that pinpoints human DNA inherited from gutters.

872
00:56:45.823 --> 00:56:48.005
Ghost ancestors.

873
00:56:48.046 --> 00:56:54.713
There have been a lot of videos and hype things about, oh, the missing link to humanity's ancestry.

874
00:56:54.753 --> 00:57:03.142
So the idea here is that, and we've talked about some of these stories before previously as well, Neanderthals and Denisovans interbred with modern history.

875
00:57:03.242 --> 00:57:07.506
Human ancestors leaving behind a telltale DNA in our genomes.

876
00:57:07.826 --> 00:57:14.753
And so if you do 23andMe or Ancestry.com, you can kind of know and see where those trace ancestry is from.

877
00:57:16.154 --> 00:57:25.763
But now the researchers at UC Berkeley have found out that we may actually have evidence for modern human interbreeding with two much older ones.

878
00:57:26.463 --> 00:57:32.227
Unknown ancestors that have not yet been recorded in any of the genomic records specifically.

879
00:57:32.267 --> 00:57:32.647
Wow.

880
00:57:32.807 --> 00:57:42.794
And the time period in which the interbreeding started was prior to the sort of the migration out of Africa, which I believe was about 800,000 years ago.

881
00:57:43.054 --> 00:57:47.938
And so this is a very big, it would be a very big deal in terms of the.

882
00:57:48.318 --> 00:57:48.638
Yeah.

883
00:57:49.078 --> 00:57:49.339
Yeah.

884
00:57:49.439 --> 00:57:51.920
If it happens before the out of Africa event.

885
00:57:51.940 --> 00:57:52.220
Yes.

886
00:57:52.401 --> 00:57:52.621
Yes.

887
00:57:53.577 --> 00:57:55.238
Then it's much more widespread, right?

888
00:57:55.278 --> 00:57:55.458
Yes.

889
00:57:55.718 --> 00:57:55.918
Yeah.

890
00:57:56.038 --> 00:57:59.860
Then it's like literally everyone who's not in Africa and maybe some in Africa.

891
00:58:00.400 --> 00:58:04.082
It appears that I believe the data point was 0.5 to 1%.

892
00:58:04.142 --> 00:58:13.986
They found traces of these two ancestral lines across every – the Eurasian, the Denisovan, Neanderthal.

893
00:58:14.087 --> 00:58:14.907
It's present –

894
00:58:15.267 --> 00:58:38.158
across everybody oh okay and so now there's obviously going to be follow-up around this but is it it is an interesting and the thing is it started uh there was this break off it started prior and then there was apparently a reconnection right before uh the rise of homo sapien and so there there seems to be some interesting there's some interesting genetic history of

895
00:58:38.858 --> 00:58:39.618
to come out of that story.

896
00:58:39.638 --> 00:58:41.159
So interesting, fascinating.

897
00:58:41.419 --> 00:58:44.020
If you would like us to cover that in more detail, let us know.

898
00:58:44.080 --> 00:58:49.781
Our last quick story reference point here, we are always going to talk about funding.

899
00:58:49.821 --> 00:58:55.283
Yesterday, the NSF announced $1.5 billion of the foundational research.

900
00:58:55.343 --> 00:59:01.985
This is the idea that every year, a couple of different times, they will have their new notices for funding opportunities.

901
00:59:02.385 --> 00:59:08.827
which define what they're funding under what dynamics and the requirements to submit your proposals.

902
00:59:09.487 --> 00:59:21.110
There's a lot of kerfuffle right now around funding because there's significant cuts that the current Trump administration is trying to make around funding generally, as well as changes to how grants are actually –

903
00:59:22.630 --> 00:59:28.132
And how grants are awarded themselves, which currently has expert review panels.

904
00:59:28.432 --> 00:59:36.135
They want to move it into being more aligned with whatever the agenda of the administration, the political administration of the time is.

905
00:59:36.215 --> 00:59:41.157
Which we covered in a previous episode about how politics is now getting intertwined into –

906
00:59:42.383 --> 00:59:48.927
Yeah, the peer review panel of experts and scientists no longer have final say.

907
00:59:48.967 --> 00:59:49.907
It's just an opinion.

908
00:59:50.148 --> 00:59:58.432
Which, again, we can talk about iterating on the process, but I think this is a hammer approach to something that requires a scalpel.

909
00:59:59.253 --> 01:00:04.276
The $1.5 billion new proposals that were announced –

910
01:00:04.496 --> 01:00:06.857
across all of the fundamental hard sciences.

911
01:00:07.037 --> 01:00:07.578
Okay.

912
01:00:07.598 --> 01:00:09.399
So this is not the social sciences per se.

913
01:00:09.419 --> 01:00:17.743
We're talking about things like biological science, expeditions and computing, electrical communications, bioengineering, manufacturing.

914
01:00:18.123 --> 01:00:29.049
One new area that I think was allocated about $30 million was emerging frontiers in wave-based computing, which has maybe some kind of tangential relationship to what we're talking about.

915
01:00:29.069 --> 01:00:30.029
Yeah, I wonder what that means.

916
01:00:31.070 --> 01:00:46.793
One of the issues people have about this is a lot of this is being framed around the golden age of X that is the overarching political narrative that is trying to be applied to a lot of research and development and the emphasis on the technological boundaries.

917
01:00:47.053 --> 01:01:06.327
You know, bolstering from a geopolitical perspective, obviously, we want to be able to do fundamental research, as we've talked about a lot, that does not necessarily have a direct through line to a practical commercial application, because some of the biggest things we have discovered in the US that have had the biggest financial impact are,

918
01:01:06.447 --> 01:01:31.074
were not decided at the point of research it was figured out after the fact and if you are curious about learning more about the history of funding in general in the u.s we have an incredible interactive explorer for funding over the last 60 years in the united states you can understand how research and development funding uh has been allocated across agencies

919
01:01:31.634 --> 01:01:40.238
even including last year's FY2026 and this year's still ongoing FY2027 funding debate.

920
01:01:40.298 --> 01:01:51.562
Looks like instead of just talking about things without knowing the information, we've given a very easy way to look at what money has actually been allocated to science and where.

921
01:01:51.943 --> 01:01:57.945
And big shout out to AAAS, who've provided the historical data sets that we've been able to build that off of.

922
01:01:58.025 --> 01:02:03.670
Now, last quick note in our break before we return to our quantum fantasticness.

923
01:02:03.710 --> 01:02:05.652
What is the – I can't remember the Marvel movie.

924
01:02:05.692 --> 01:02:07.834
Quantum – Quantumania.

925
01:02:07.914 --> 01:02:08.314
There it is.

926
01:02:08.834 --> 01:02:09.955
That's the one that I didn't see.

927
01:02:09.975 --> 01:02:12.598
Quantumania, and it was apparently terrible.

928
01:02:12.658 --> 01:02:13.679
So we don't care about that.

929
01:02:13.699 --> 01:02:18.483
But we have one correction from our previous episode, which was on the Riemann Hypothesis.

930
01:02:18.623 --> 01:02:18.903
Yes.

931
01:02:19.163 --> 01:02:26.929
So the previous episode, a lot of you saw it, and most of it I'm very proud of.

932
01:02:27.830 --> 01:02:38.598
There's one segment where I think I could have done better, and it was when we were discussing some of Claude's results, and specifically this particular graphic came up.

933
01:02:39.905 --> 01:02:50.450
As background, Claude made some progress in a related problem to the Riemann hypothesis, where the Riemann hypothesis is where are the zeros of the Riemann zeta function?

934
01:02:51.150 --> 01:02:57.353
Are they all on the critical line where the real part of the zeros is one half?

935
01:02:57.773 --> 01:02:59.934
Now, Claude showed...

936
01:03:00.567 --> 01:03:14.254
that the previous bound of something like 44% had gone up to 67%, which means that 67% of all of the non-trivial zeros are on that line.

937
01:03:14.274 --> 01:03:14.914
Critical line.

938
01:03:15.234 --> 01:03:20.517
And I mistakenly said that if we get to 100%, that's going to be the Riemann hypothesis.

939
01:03:20.597 --> 01:03:22.038
And it's because that graphic...

940
01:03:22.998 --> 01:03:28.242
showed 100% line over there, and it said Riemann hypothesis, and I just wasn't really thinking.

941
01:03:28.803 --> 01:03:33.106
It's a lot richer than that, because this is a statistical argument, right?

942
01:03:33.926 --> 01:03:40.671
And you actually brought it up earlier when you said that, you know, with infinities, it's hard to talk about percentages.

943
01:03:41.052 --> 01:03:49.878
Like, when we say that 67%, or let's say two-thirds, let's say two-thirds of all zeros are on the critical line,

944
01:03:51.668 --> 01:03:52.008
G.H.

945
01:03:52.048 --> 01:03:55.689
Hardy had already proved that there are an infinite number of zeros on the critical line.

946
01:03:55.709 --> 01:04:00.311
So what does it mean for the infinite number of zeros to only at least be two-thirds?

947
01:04:00.631 --> 01:04:05.732
Well, what that means is two out of three in that infinite set are on the line.

948
01:04:05.812 --> 01:04:07.653
That's what Claude is saying, right?

949
01:04:07.673 --> 01:04:15.195
There's an infinite set, and just like how one out of two of the infinite set of natural numbers are even numbers, one can say—

950
01:04:16.335 --> 01:04:20.738
or 2 out of 3 of all of the numbers are not multiples of 3.

951
01:04:21.218 --> 01:04:22.179
That's another way of saying it.

952
01:04:22.439 --> 01:04:29.123
That's another way of saying, like, in the infinite set, 2 out of 3 of all of the elements are going to be on that line, right?

953
01:04:30.324 --> 01:04:34.527
And then I mistakenly said that if we get to 100, that'll mean the Riemann hypothesis is true.

954
01:04:34.567 --> 01:04:36.028
That's not the case, right?

955
01:04:36.068 --> 01:04:37.008
Because of infinities.

956
01:04:37.589 --> 01:04:42.872
So you could have, for example, an infinite number of zeros on the critical line,

957
01:04:45.974 --> 01:05:13.723
somewhere else that would still give you a hundred percent on the critical line but the reman hypothesis would still be false because not every zero is on the critical line statistically we can reach a hundred and you still haven't proven the reman hypothesis that's the point and so ai you're still you're still not there there's a song if i find it i'll play it in the next episode because now there's like counterculture rap music about like wanting data centers in your neighborhood

958
01:05:14.003 --> 01:05:14.483
No way.

959
01:05:14.503 --> 01:05:16.865
But it's like they don't really want a data center in the neighborhood.

960
01:05:17.345 --> 01:05:19.927
But some people will know what I'm talking about.

961
01:05:19.947 --> 01:05:22.069
It's like, I want a data center in my neighborhood.

962
01:05:22.709 --> 01:05:24.791
I need a data center in my neighborhood.

963
01:05:25.371 --> 01:05:27.092
I want a data center in my town.

964
01:05:27.813 --> 01:05:30.055
Please put a data center in my neighborhood.

965
01:05:30.455 --> 01:05:33.097
That way, my ramp might actually go down.

966
01:05:33.497 --> 01:05:34.958
I don't care if I lose my hearing.

967
01:05:35.478 --> 01:05:40.662
Like, I don't care if my water, like, you know, and it's like, obviously, yeah, it's like satire, satire around it.

968
01:05:40.782 --> 01:05:47.826
But, um, it's funny how culture and these issues related to AI are so intertwined.

969
01:05:47.846 --> 01:05:49.087
But we, after we're,

970
01:05:49.467 --> 01:05:50.989
quite a fun break.

971
01:05:51.509 --> 01:05:53.611
Again, the best show in science.

972
01:05:54.011 --> 01:06:00.898
Not only do you get a deep dive, you get some background context on the latest happenings at the Frontier.

973
01:06:01.338 --> 01:06:14.070
No other show provides you the best Frontier breaking news science experience with a depth of understanding where you're going to walk away not only learning something, but understanding the context

974
01:06:14.510 --> 01:06:15.991
in which these discoveries were made.

975
01:06:16.011 --> 01:06:24.037
And so we're going to jump back now into our breakdown of quantum computing in our part one of our two-part deep dive.

976
01:06:25.078 --> 01:06:29.121
So we left off with Feynman's keynote address at that conference.

977
01:06:29.241 --> 01:06:37.527
And as I said, you know, Feynman's keynote address was amazing, but that's not really why we have a trillion-dollar ecosystem now.

978
01:06:39.088 --> 01:06:42.270
He approached quantum computing from this physical modeling perspective.

979
01:06:43.772 --> 01:06:58.769
At the same time, David Deutsch in England, he formalized the mathematics of quantum computational complexity in a 1985 paper, Quantum Theory and the Church-Turing Principle and the Universal Quantum Computer.

980
01:07:00.130 --> 01:07:00.731
If you notice...

981
01:07:01.815 --> 01:07:07.719
It is communicated by Roger Penrose, fellow of the Royal Society, to the proceedings of the Royal Society.

982
01:07:07.759 --> 01:07:18.406
So Roger Penrose is also in this story, the great mathematician and physicist who won the Nobel Prize for his proof that black holes are definitely a reality.

983
01:07:19.647 --> 01:07:27.772
So he shows, David Deutsch, in this paper, he defines the universal quantum Turing machine.

984
01:07:29.157 --> 01:07:33.379
And that establishes the kind of quantum circuit model that we see today.

985
01:07:33.740 --> 01:07:38.403
When we look at quantum algorithms and you have these blocks, we're going to see some of these later on.

986
01:07:39.484 --> 01:07:46.949
The logic operations are now represented by unitary matrices, the kinds of Toffoli gates and things like that that we were talking about earlier.

987
01:07:47.549 --> 01:07:49.851
These are reversible logic gates.

988
01:07:50.791 --> 01:07:50.971
And...

989
01:07:52.072 --> 01:07:55.615
They can act on a register of quantum bits or qubits.

990
01:07:56.255 --> 01:07:59.077
So this is where he's establishing, you know, I've got a bit.

991
01:07:59.417 --> 01:08:01.719
The computer is made out of a bunch of quantum bits.

992
01:08:02.319 --> 01:08:08.443
I act on these bits with unitary matrices, unitary transformations, and I can start computing things.

993
01:08:09.124 --> 01:08:17.830
Is this the first building the bridge from this theory and the software of the algorithm to now how that interacts with the substrate of a hardware?

994
01:08:17.870 --> 01:08:18.050
Yeah.

995
01:08:18.390 --> 01:08:25.492
Yeah, in some sense, it's more like it's taking the building blocks that people had made earlier with the gates and things like that.

996
01:08:25.612 --> 01:08:29.313
And Feynman saying that, you know, you've got these two state systems.

997
01:08:29.413 --> 01:08:34.174
He's like, I can now build a Turing machine that'll do stuff for me.

998
01:08:34.374 --> 01:08:37.235
The framework of how you would be able to make this actually productive.

999
01:08:37.335 --> 01:08:38.036
Yes, exactly.

1000
01:08:38.076 --> 01:08:39.338
These concepts of productive systems.

1001
01:08:39.378 --> 01:08:40.379
Yeah, yeah, exactly.

1002
01:08:40.720 --> 01:08:48.951
And side note, Deutsche's academic pursuit is driven by a commitment to the many worlds interpretation of quantum mechanics.

1003
01:08:49.311 --> 01:08:51.714
He is fanatical about this interpretation.

1004
01:08:51.755 --> 01:08:53.237
He thinks this is the only way to go.

1005
01:08:53.657 --> 01:08:54.078
And, you know...

1006
01:08:54.758 --> 01:08:57.959
There's a lot of people that are very smart out there that are saying this is the only way to go.

1007
01:08:58.939 --> 01:09:09.463
During his Oxford studies as a graduate student, he met Bryce DeWitt, who's a very famous theoretical physicist who was a collaborator of John Wheeler at Princeton.

1008
01:09:09.543 --> 01:09:13.664
I think DeWitt was actually at the Institute for Advanced Studies, so he was not at Princeton at the time.

1009
01:09:14.084 --> 01:09:15.885
But he and Wheeler used to talk a lot.

1010
01:09:15.965 --> 01:09:23.727
And Wheeler was the Ph.D. advisor of Hugh Everett, who's the guy behind the Everett theory.

1011
01:09:23.987 --> 01:09:25.668
hypothesis of many worlds, right?

1012
01:09:26.029 --> 01:09:38.799
Everett went on to do RAND and national security apparatus type stuff because he got basically shot down by Niels Bohr when he went and visited Copenhagen.

1013
01:09:39.220 --> 01:09:39.360
But

1014
01:09:40.656 --> 01:09:45.281
Wheeler kept the idea alive of Everettian mechanics.

1015
01:09:45.321 --> 01:09:50.946
Bryce DeWitt did a few things with Wheeler about that many worlds interpretation.

1016
01:09:51.247 --> 01:09:56.252
And they met at a pizza parlor in London, Deutsch and DeWitt.

1017
01:09:56.612 --> 01:09:59.375
And that's when Deutsch got into this many worlds interpretation.

1018
01:09:59.435 --> 01:10:00.977
And he got really into it.

1019
01:10:01.397 --> 01:10:04.300
And in Deutsch's view, when a quantum computer processes

1020
01:10:04.767 --> 01:10:20.427
like these computational states simultaneously, what it's actually doing, this is Deutsch's interpretation, is that the calculations are executed across all of the different branches of your many worlds wave function

1021
01:10:21.665 --> 01:10:22.746
In this like multiverse.

1022
01:10:23.286 --> 01:10:27.729
And then they recombine with quantum interference when we like make an observation.

1023
01:10:27.949 --> 01:10:30.190
It's a form of interdimensional travel.

1024
01:10:30.290 --> 01:10:30.550
Yeah.

1025
01:10:30.630 --> 01:10:31.171
Effectively.

1026
01:10:31.331 --> 01:10:32.752
Effectively in some sense.

1027
01:10:32.852 --> 01:10:36.214
And using the cinematic parlance that people think about.

1028
01:10:36.794 --> 01:10:38.635
It's we're going.

1029
01:10:38.655 --> 01:10:42.518
Yeah, we're like computing in multiple universes and then we're bringing it all together.

1030
01:10:42.558 --> 01:10:43.098
All together.

1031
01:10:43.178 --> 01:10:43.418
Yeah.

1032
01:10:43.538 --> 01:10:47.501
And we're using the extra compute of these other universes or extra whatever.

1033
01:10:47.521 --> 01:10:47.621
Yeah.

1034
01:10:48.081 --> 01:10:48.501
Whatever.

1035
01:10:48.541 --> 01:10:49.061
Yeah, yeah, yeah.

1036
01:10:49.081 --> 01:10:49.742
That's what he thinks.

1037
01:10:49.982 --> 01:11:06.489
And then, you know, that's how we can do it where it seems like, ah, it's so funny because this is like, obviously, Evredian ideology, as I like to call it, is one of the abuses –

1038
01:11:09.367 --> 01:11:28.420
in uh entertainment yeah that is where quantum and then multi many worlds excuse me get kind of conflated and then spins out of control yeah yeah because with many worlds like i mean you could just say anything right if you're if you're in hollywood you just yeah uh multiverse right

1039
01:11:29.280 --> 01:11:42.428
And this is Marvel has got themselves in a problem right now because, because of all the stuff that they've done and they've basically said, well, no, Iron Man only died in this universe, but not in the many other universes.

1040
01:11:42.548 --> 01:11:43.628
Dude, Robert Downey Jr.

1041
01:11:43.688 --> 01:11:46.310
I think you made enough money, right?

1042
01:11:46.390 --> 01:11:53.394
Anyways, the reason why I bring this up is because Hartmut Nevin, who is at Google quantum AI, I think he's one of the heads there.

1043
01:11:53.814 --> 01:11:54.995
He, he,

1044
01:11:55.834 --> 01:11:58.398
wrote a blog post about Google's Willow Chip.

1045
01:11:58.639 --> 01:12:06.472
Google's Willow Chip is this latest of Google's quantum computing platforms where the performance there...

1046
01:12:07.738 --> 01:12:09.659
on this benchmark was astonishing, right?

1047
01:12:09.719 --> 01:12:20.387
And so what Hartman Nevin wrote is that it performed a computation in under five minutes that would take today's supercomputers 10 septillion years.

1048
01:12:20.627 --> 01:12:26.872
Okay, if you want to write it out, that's 10 with, I don't know, I'm not going to count however many zeros there are, right?

1049
01:12:26.992 --> 01:12:34.057
But crucially, he said, this mind-boggling number exceeds known timescales in physics and vastly exceeds the age of the universe—

1050
01:12:34.537 --> 01:12:43.662
It lends credence to the notion that quantum computation occurs in many parallel universes in line with the idea that we live in a multiverse, a prediction first made by David Deutsch.

1051
01:12:43.962 --> 01:12:49.525
And if you go back to that overlay, the media took over, right?

1052
01:12:49.585 --> 01:12:52.027
And they're like, Google says it appears to have accessed quantum.

1053
01:12:52.467 --> 01:13:08.712
parallel universes i remember when this came out and people were texting me because i'm like you know they're the only physicist you're the quantum guy yeah yeah yeah and they're like they're like dude we live in a multiverse i'm like no no we don't okay i mean maybe shit i don't know but

1054
01:13:09.552 --> 01:13:13.395
I don't think this proves that we live in a multiverse.

1055
01:13:13.775 --> 01:13:18.699
It's just funny that one of the heads of Google Quantum AI is also on this hype train, right?

1056
01:13:18.999 --> 01:13:21.021
So he said that this is proof of that.

1057
01:13:21.201 --> 01:13:21.881
I don't think so.

1058
01:13:22.141 --> 01:13:24.163
There's a lot of people out there that don't think so.

1059
01:13:24.663 --> 01:13:27.305
The Copenhagen interpretation could be just as valid.

1060
01:13:27.566 --> 01:13:30.047
I mean, it's all just like philosophy at this point, right?

1061
01:13:30.127 --> 01:13:30.908
About which one is...

1062
01:13:31.208 --> 01:13:38.374
I don't know if there's a way to tell if we're in a multiverse or if we're just... Copenhagen is just the way it is and the universe just...

1063
01:13:39.234 --> 01:14:01.292
is weird unless the aliens come from the other universe and they figure out a way yeah yeah and then they come and tell us and they like if an alien came and told us that i i'm from the other okay all right i'm from timeline two yeah it's like okay yeah like i'm from earth but like we look different it's okay cool i'm just saying you know like so all right so david deutsch

1064
01:14:02.266 --> 01:14:07.809
He wants to prove that a quantum computer could perform tasks faster than any classical machine.

1065
01:14:08.410 --> 01:14:14.073
Because so far, Feynman has said this in his talk.

1066
01:14:14.173 --> 01:14:17.655
He said, I mean, clearly, we can't store this many states.

1067
01:14:19.516 --> 01:14:22.558
But Deutsch wants to design a quantum algorithm that really shows this.

1068
01:14:23.239 --> 01:14:29.863
And he designs the first quantum algorithm in 1985, and it's expanded alongside with Richard Joza in 1992.

1069
01:14:29.883 --> 01:14:30.003
Okay.

1070
01:14:31.763 --> 01:14:32.943
This is the paper that comes out.

1071
01:14:33.484 --> 01:14:35.064
Again, Proceedings of Royal Society.

1072
01:14:36.324 --> 01:14:45.967
It's a simple enough problem that I think I could describe it in enough detail on this podcast and not lose some of the essence of what's going on in the quantum solution.

1073
01:14:46.047 --> 01:14:46.307
Okay?

1074
01:14:46.647 --> 01:14:48.188
And I'm going to go ahead and give you the punchline.

1075
01:14:48.268 --> 01:14:48.528
Okay.

1076
01:14:48.648 --> 01:14:52.829
It's a toy problem, but it's one where a classical computer would take...

1077
01:14:53.812 --> 01:15:02.256
exponentially an amount of time to get to an answer with respect to the size of the input, but a quantum computer can one shot it.

1078
01:15:02.697 --> 01:15:03.317
Okay.

1079
01:15:03.537 --> 01:15:05.478
So we're going from exponential to one shot.

1080
01:15:05.578 --> 01:15:06.018
One shot.

1081
01:15:06.419 --> 01:15:06.699
Okay.

1082
01:15:06.819 --> 01:15:08.320
Using a quantum algorithm.

1083
01:15:08.520 --> 01:15:09.180
Here's the problem.

1084
01:15:09.460 --> 01:15:09.680
Okay.

1085
01:15:10.981 --> 01:15:20.246
So you're given a black box function and this black box function is going to take inputs of N digit binary numbers.

1086
01:15:20.266 --> 01:15:20.506
Okay.

1087
01:15:21.764 --> 01:15:24.947
and give back a single digit, either a zero or a one.

1088
01:15:25.007 --> 01:15:34.956
So if n is like two, it can give, it takes in as input, you know, either zero zero zero one one zero one one, and it spits out either a zero or a one.

1089
01:15:35.256 --> 01:15:37.899
Now in essence, this could be any n digit binary number.

1090
01:15:37.979 --> 01:15:38.919
n could be very large.

1091
01:15:38.939 --> 01:15:43.684
So n could be like that giant matrix of zeros and ones that goes into this black box function.

1092
01:15:43.824 --> 01:15:46.046
I don't know how this black box function works.

1093
01:15:46.506 --> 01:15:48.108
Okay, it's a black box.

1094
01:15:48.648 --> 01:15:51.389
I stick an input and I get an output of either 0 or 1.

1095
01:15:51.549 --> 01:15:58.731
This is similar to the AND gate we talked about at the beginning in terms of you have two, then you only have one input on the other side.

1096
01:15:58.911 --> 01:16:00.051
So it's not reversible.

1097
01:16:00.071 --> 01:16:00.291
Yes.

1098
01:16:00.551 --> 01:16:01.751
Yeah, this is not reversible.

1099
01:16:01.871 --> 01:16:02.512
Yes, very good.

1100
01:16:02.632 --> 01:16:07.713
And an AND gate would be like 0, 0 goes to 0, 0, 1 goes to 0, 0, 1.

1101
01:16:07.733 --> 01:16:09.773
But this is even worse because it only goes to one answer.

1102
01:16:09.833 --> 01:16:11.254
Yeah, it only goes to one answer.

1103
01:16:11.714 --> 01:16:14.054
And no matter how big the thing is.

1104
01:16:14.435 --> 01:16:15.895
And I don't know if it's an AND gate.

1105
01:16:16.555 --> 01:16:17.536
Right.

1106
01:16:17.616 --> 01:16:18.556
It's a black box.

1107
01:16:18.656 --> 01:16:20.657
I don't know what it's doing in there.

1108
01:16:20.777 --> 01:16:21.697
That's the point.

1109
01:16:21.797 --> 01:16:26.079
The black box replaces this concept of an and gate in terms of being able to be well defined.

1110
01:16:26.139 --> 01:16:26.360
Yeah.

1111
01:16:26.500 --> 01:16:28.681
And gate, I know exactly what the truth table is.

1112
01:16:28.781 --> 01:16:30.401
Here, I don't know what the truth table is.

1113
01:16:30.822 --> 01:16:31.002
Right?

1114
01:16:31.402 --> 01:16:33.383
So I want to make it simple.

1115
01:16:33.423 --> 01:16:34.983
So let's just consider n equals 2.

1116
01:16:35.304 --> 01:16:35.584
Okay.

1117
01:16:35.644 --> 01:16:36.404
As I was saying, right?

1118
01:16:36.464 --> 01:16:36.624
Yep.

1119
01:16:36.784 --> 01:16:37.625
So in n equals 2.

1120
01:16:38.645 --> 01:16:39.825
We'll go to the next overlay.

1121
01:16:40.206 --> 01:16:43.567
So at n equals 2, there's four different numbers that I can feed in.

1122
01:16:43.787 --> 01:16:47.148
I can either feed in 00, 01, 10, or 11.

1123
01:16:48.268 --> 01:17:00.152
Those are going to go in one at a time into this black box, and that black box is going to make an output, and it's going to tell me, hey, if you give me this input, the output is either 0 or 1, depending on whatever I gave as input.

1124
01:17:01.032 --> 01:17:02.673
I'm given another promise.

1125
01:17:03.668 --> 01:17:07.771
I'm given a promise that this function is either constant or it's balanced.

1126
01:17:08.312 --> 01:17:09.213
What do I mean by that?

1127
01:17:09.773 --> 01:17:18.139
So it's either a constant function in the sense that no matter what the input is, my output is always going to be 0 or it's always going to be 1.

1128
01:17:19.040 --> 01:17:20.621
There's only two such functions, right?

1129
01:17:20.681 --> 01:17:25.105
It's either all 1s, so no matter what my input is, it's going to give out a 1.

1130
01:17:25.625 --> 01:17:28.507
No matter what my input is, it's going to give out a 0, right?

1131
01:17:28.547 --> 01:17:29.308
It's one of these two.

1132
01:17:30.849 --> 01:17:32.130
Or it is balanced.

1133
01:17:32.250 --> 01:17:38.816
A balanced function means that exactly half of the inputs map to zero and exactly half of the inputs map to one.

1134
01:17:39.176 --> 01:17:46.823
There's several, not several, there's only six examples for a two-bit input.

1135
01:17:47.083 --> 01:17:51.066
Because, you know, it's four choose two is going to give you six.

1136
01:17:51.126 --> 01:17:52.627
Two of these I've described over here.

1137
01:17:52.687 --> 01:17:55.149
The first one I think is like first bit only.

1138
01:17:55.470 --> 01:17:57.111
Basically, whatever the first bit is,

1139
01:17:58.272 --> 01:17:59.233
That's what it's going to output.

1140
01:17:59.373 --> 01:18:01.494
So for 0, 0, the first bit is 0.

1141
01:18:02.174 --> 01:18:03.775
This black box is going to output 0.

1142
01:18:04.016 --> 01:18:05.597
For 0, 1, it's going to output 0.

1143
01:18:05.877 --> 01:18:07.478
For 1, 0, the first bit is now 1.

1144
01:18:07.498 --> 01:18:09.039
So it's going to output 1.

1145
01:18:09.459 --> 01:18:10.740
For 1, 1, it's going to output 1.

1146
01:18:11.040 --> 01:18:15.102
Notice there's two 0s that come out and there's two 1s that come out out of the 4.

1147
01:18:15.162 --> 01:18:16.303
Because the first input...

1148
01:18:17.163 --> 01:18:18.364
is whatever the thing is.

1149
01:18:18.584 --> 01:18:21.606
And the function doesn't even look at what the second input is.

1150
01:18:21.646 --> 01:18:22.786
It's just like, oh, the first one is zero.

1151
01:18:22.846 --> 01:18:23.967
I'm just going to spit that out.

1152
01:18:24.007 --> 01:18:26.248
So that's one version of a balanced function.

1153
01:18:26.668 --> 01:18:31.691
Another version of a balanced function is an XOR, exclusive OR, meaning the bits are different.

1154
01:18:32.191 --> 01:18:34.553
So if the bits are different, I'm going to output a 1.

1155
01:18:34.953 --> 01:18:36.814
If the bits are the same, I'm going to output a 0.

1156
01:18:36.874 --> 01:18:40.177
Notice if it's 0, 0, I output a 0 because they're the same.

1157
01:18:40.457 --> 01:18:42.679
If it's 1, 1, I output a 0 because they're the same.

1158
01:18:43.219 --> 01:18:45.160
If it's 0, 1 or 1, 0, I output a 1.

1159
01:18:45.480 --> 01:18:45.701
Okay?

1160
01:18:45.961 --> 01:18:48.663
So again, this is balanced because there's two 0s and two 1s.

1161
01:18:48.943 --> 01:18:50.624
There's six such functions.

1162
01:18:50.704 --> 01:18:51.665
I've only shown you two.

1163
01:18:51.905 --> 01:18:52.165
Got it.

1164
01:18:52.345 --> 01:18:52.566
Okay.

1165
01:18:52.686 --> 01:18:53.786
So these are two examples.

1166
01:18:53.887 --> 01:18:54.807
These are two examples.

1167
01:18:54.907 --> 01:19:00.151
And here there's like a systematic rule, but imagine for like N digits, you don't need a systematic rule.

1168
01:19:00.171 --> 01:19:08.258
There could just be whoever designed the black box chose half of the inputs at random and be like these guys mapped to zero and half of the inputs these guys mapped to one.

1169
01:19:08.798 --> 01:19:09.058
Okay.

1170
01:19:09.158 --> 01:19:12.521
And it has its own basically mapping key that is whatever.

1171
01:19:12.661 --> 01:19:13.502
Yes, there's a map.

1172
01:19:13.562 --> 01:19:13.942
Exactly.

1173
01:19:13.962 --> 01:19:15.523
There's a mapping key that we don't know.

1174
01:19:15.984 --> 01:19:16.184
Okay.

1175
01:19:16.204 --> 01:19:16.684
That's the point.

1176
01:19:17.505 --> 01:19:20.907
Your job is to figure out who am I?

1177
01:19:21.908 --> 01:19:23.750
Am I balanced or am I constant?

1178
01:19:23.850 --> 01:19:25.211
I gave you two choices, right?

1179
01:19:25.291 --> 01:19:27.413
I'm either balanced or I'm constant.

1180
01:19:28.474 --> 01:19:33.358
And I give you this black box to play with where all you can do is put in stuff and you get out an answer.

1181
01:19:35.020 --> 01:19:45.128
The question is how many queries, how many times do I need to press play on the black box with whatever input I give it to determine if it's balanced or constant?

1182
01:19:45.148 --> 01:19:46.329
That's the idea.

1183
01:19:46.389 --> 01:19:47.110
That's the problem.

1184
01:19:47.530 --> 01:19:48.872
So how would I do it classically?

1185
01:19:49.192 --> 01:19:49.352
Yep.

1186
01:19:50.623 --> 01:19:52.505
If I want to do it classically, it's actually...

1187
01:19:53.987 --> 01:19:56.049
I mean, there's only one choice that I have, right?

1188
01:19:56.089 --> 01:20:02.215
It's like I feed in a number, I get an output, I use my logical brain to figure out what it is.

1189
01:20:04.212 --> 01:20:10.115
Classically, what I do first is I just test 0, 0, and suppose I get a 0.

1190
01:20:10.795 --> 01:20:12.996
And I test 0, 1, and suppose I get a 0.

1191
01:20:13.676 --> 01:20:17.818
I cannot claim that it's balanced or constant because it could be both, right?

1192
01:20:18.378 --> 01:20:24.741
It could be that the first two go to 0 and the next two go to 1, and I've only checked the first two.

1193
01:20:24.941 --> 01:20:26.342
Or it could be that all of them go to 0.

1194
01:20:26.642 --> 01:20:28.322
So I need to check that third one.

1195
01:20:30.023 --> 01:20:37.152
At this point after two, there are arguments that it could be constant or it could be balanced.

1196
01:20:37.172 --> 01:20:42.939
Because you've not yet had enough data to rule out one or the other.

1197
01:20:43.080 --> 01:20:43.520
Exactly.

1198
01:20:43.760 --> 01:20:46.824
So I need to do that third query to check.

1199
01:20:47.922 --> 01:20:49.364
I need to check one zero.

1200
01:20:49.644 --> 01:20:54.069
And if one zero comes out as zero, then I know that it's constant, right?

1201
01:20:54.409 --> 01:20:56.191
Because I only have those two choices.

1202
01:20:56.571 --> 01:20:59.474
And I've already queried three, and they're all the same, so it has to be constant.

1203
01:20:59.694 --> 01:21:06.001
On the other hand, if the third one comes out to be one, then I know that it's balanced, because I know that the other guy is also going to be one.

1204
01:21:06.081 --> 01:21:07.762
I don't need to check the other guy, right?

1205
01:21:08.083 --> 01:21:09.584
Now, you could say, well, what if...

1206
01:21:10.926 --> 01:21:18.954
You know, in the case that it's balanced and the first and the third inputs go to zero and the second and the fourth go to one, right?

1207
01:21:20.195 --> 01:21:26.582
Worst case scenario, what if I randomly picked the other stuff and I could choose, right?

1208
01:21:26.742 --> 01:21:27.002
Well...

1209
01:21:27.663 --> 01:21:36.068
In the worst case scenario, the guy who's designing the black box knows exactly how you're going to check the first few inputs, right?

1210
01:21:36.189 --> 01:21:44.214
And so if you're trying to just get – like the best case scenario is I just pick two and I get lucky.

1211
01:21:44.374 --> 01:21:45.915
One of them is zero and one of them is one.

1212
01:21:46.235 --> 01:21:49.977
And then I'm like, oh, it has to be balanced because it's definitely not constant, right?

1213
01:21:50.197 --> 01:21:50.758
And so I'm done.

1214
01:21:51.218 --> 01:21:57.723
But the guy who's building the black box could know exactly your schema of which bits, which bit string you're going to test.

1215
01:21:58.023 --> 01:22:01.145
To make it maximally difficult for you to find the answer.

1216
01:22:01.385 --> 01:22:01.846
Yeah.

1217
01:22:01.946 --> 01:22:05.908
So worst case scenario, you always have to do exactly half plus one.

1218
01:22:06.169 --> 01:22:06.389
Yeah.

1219
01:22:06.589 --> 01:22:06.769
Right?

1220
01:22:07.009 --> 01:22:07.169
Yeah.

1221
01:22:07.329 --> 01:22:07.549
Okay.

1222
01:22:07.570 --> 01:22:08.250
I get what you're saying.

1223
01:22:08.610 --> 01:22:08.890
Okay.

1224
01:22:08.950 --> 01:22:14.875
So I have to do three in this case where there's four bit strings.

1225
01:22:15.275 --> 01:22:15.475
Okay.

1226
01:22:15.795 --> 01:22:18.157
How would I do this with quantum mechanics?

1227
01:22:20.190 --> 01:22:28.672
With quantum mechanics, what Deutsch-Joseph came up with is they said, actually, we could pass a superposition of all four versions.

1228
01:22:29.953 --> 01:22:34.454
Remember, in Bell's theorem, right, all four versions are not together, right?

1229
01:22:34.514 --> 01:22:36.755
Like, or sorry, cannot be separated.

1230
01:22:37.255 --> 01:22:40.416
So I could create a superposition of all of the four states.

1231
01:22:40.476 --> 01:22:44.917
I could create a superposition of 0, 0, 0, 1, 1, 0, and 1, 1.

1232
01:22:46.398 --> 01:22:47.358
And I pass that.

1233
01:22:48.344 --> 01:22:51.106
entire thing through the black box.

1234
01:22:51.786 --> 01:22:55.549
Now, I can't separate these out, and the black box is going to have to interact with the whole thing, right?

1235
01:22:56.225 --> 01:23:00.166
And now, this black box function, what is it going to do to the superposition?

1236
01:23:00.266 --> 01:23:03.127
It is going to act on it with that black box function.

1237
01:23:03.447 --> 01:23:07.088
There's going to be some quantum version of the black box function.

1238
01:23:07.368 --> 01:23:12.929
That's, again, this is a theory gimmick where it's like, oh, there's a way to just make it quantum mechanical, right?

1239
01:23:13.769 --> 01:23:16.590
It's like an oracle is what they call it.

1240
01:23:17.150 --> 01:23:23.752
So when we do that, what I'm going to do is implement this black box function in such a way that whenever...

1241
01:23:24.862 --> 01:23:28.624
the input goes to 0, I'm going to leave it alone.

1242
01:23:29.745 --> 01:23:36.610
But if the input goes to 1, I am going to introduce a negative sign in front of that qubit.

1243
01:23:36.650 --> 01:23:41.673
Like I'm going to attach a negative 1 as the amplitude in front of that qubit.

1244
01:23:42.093 --> 01:23:43.734
So what happens here?

1245
01:23:45.776 --> 01:23:52.300
If it is balanced, all of them are going to have the same sign.

1246
01:23:53.447 --> 01:23:53.648
Right?

1247
01:23:54.388 --> 01:23:58.211
And maybe we go to the next... Because that'll show it.

1248
01:23:58.231 --> 01:23:58.471
Yes.

1249
01:23:58.771 --> 01:24:01.053
So if it's constant, everything is going to be the same.

1250
01:24:01.293 --> 01:24:01.413
Right?

1251
01:24:01.433 --> 01:24:06.937
Because it's going to be plus, plus, plus, plus, and minus, minus, minus, minus, depending on whether it's a zero or a one that it gets mapped to.

1252
01:24:07.477 --> 01:24:08.358
If it's balanced...

1253
01:24:08.378 --> 01:24:11.700
This is going to be... Then two are going to be plus and two are going to be minus.

1254
01:24:11.780 --> 01:24:11.920
Yeah.

1255
01:24:11.980 --> 01:24:13.441
And they're going to interfere with each other.

1256
01:24:13.542 --> 01:24:15.203
And this is where the interference comes in.

1257
01:24:15.783 --> 01:24:15.983
Right?

1258
01:24:16.564 --> 01:24:20.606
So if it's constant, I'm going to get constructive interference.

1259
01:24:20.727 --> 01:24:20.907
Yeah.

1260
01:24:20.927 --> 01:24:21.247
Yeah.

1261
01:24:21.487 --> 01:24:24.970
And if it is balanced, I'm going to get destructive interference.

1262
01:24:24.990 --> 01:24:25.670
Because they cancel out.

1263
01:24:25.730 --> 01:24:25.911
Yeah.

1264
01:24:25.931 --> 01:24:26.951
Because they're different.

1265
01:24:28.152 --> 01:24:33.957
And this is the key to almost every single, actually every single quantum algorithm.

1266
01:24:34.497 --> 01:24:41.483
Every single quantum algorithm uses this idea of constructive and destructive interference to do the computation.

1267
01:24:41.983 --> 01:24:43.605
So now you've one-shotted it.

1268
01:24:44.225 --> 01:24:46.428
This is basically your 0 or 1 now.

1269
01:24:46.688 --> 01:24:47.509
Yeah.

1270
01:24:47.529 --> 01:24:52.254
And if you get constructive interference, I know that it's balanced.

1271
01:24:52.875 --> 01:24:57.760
And if I get destructive interference, no, if I get constructive interference, I know that it's constant.

1272
01:24:58.902 --> 01:25:03.867
And if I get destructive interference, I know that it's balanced because everything interfered.

1273
01:25:05.469 --> 01:25:11.395
And so is the idea that, you know, because effectively what we're saying is the black box is a quantum system.

1274
01:25:11.955 --> 01:25:13.016
Because we can't really know.

1275
01:25:13.076 --> 01:25:17.881
Yeah, the black box is us implementing the function as a quantum algorithm.

1276
01:25:18.382 --> 01:25:18.622
Right.

1277
01:25:18.742 --> 01:25:19.002
Okay.

1278
01:25:19.302 --> 01:25:21.284
And we ultimately want to make...

1279
01:25:22.045 --> 01:25:34.719
the black box, which we may not really know what's happening inside it, but we still need to have some level of deterministic output from it to make it functional as a computing system.

1280
01:25:34.899 --> 01:25:41.186
Yeah, and the point here is because we know this constraint of it's either balanced or constant.

1281
01:25:41.206 --> 01:25:41.326
Yes.

1282
01:25:41.346 --> 01:25:41.467
Yes.

1283
01:25:42.390 --> 01:25:47.553
We can now implement this black box and say that it's only going to flip the phase.

1284
01:25:47.573 --> 01:25:51.056
This is called phase flipping of those places where the output is one.

1285
01:25:51.676 --> 01:25:54.858
And that's why we're going to get that constructive and destructive interference.

1286
01:25:55.179 --> 01:25:57.540
Now, I want to connect this to a physical reality.

1287
01:25:57.640 --> 01:25:57.800
Okay.

1288
01:25:57.940 --> 01:25:58.201
Okay.

1289
01:25:58.461 --> 01:26:00.582
Because it's a bit weird, right?

1290
01:26:01.002 --> 01:26:06.086
So let's just talk about to really understand why the quantum mechanics lets us do this.

1291
01:26:06.586 --> 01:26:09.388
Let's consider just a quantum interference experiment, okay?

1292
01:26:09.468 --> 01:26:25.257
And I want to take the double-slit experiment, which we've discussed a lot in this podcast, and I want to try to create a version of the double-slit experiment that computes my Deutsch-Joseph problem, okay?

1293
01:26:25.757 --> 01:26:30.440
Now, to introduce the double-slit experiment, you've got a laser with coherent light.

1294
01:26:31.120 --> 01:26:33.482
That light falls on two slits,

1295
01:26:34.438 --> 01:26:54.832
that two slits meaning there's like a wall with two holes in it the light goes through it interferes with the wall so the wall doesn't let it through except for those two holes and those two holes then let the light through the light from one hole is going to interfere with the light in the other hole and if i were to cover up just one of the holes then i would get

1296
01:26:55.252 --> 01:27:00.056
a lump of P1 or P2, that's the first sort of two Gaussians that I see.

1297
01:27:00.356 --> 01:27:08.223
But if I don't cover either one and I let the light go through both, then I get this interference pattern, right?

1298
01:27:08.463 --> 01:27:16.510
Where in the middle, you're going to get a really bright spot because the light from one hole and the light from the other hole are sort of constructively interfering.

1299
01:27:17.050 --> 01:27:25.417
And right around there, I'm going to get destructive interference because the light from one hole is coinciding with the trough of the wave of another hole.

1300
01:27:25.677 --> 01:27:27.199
And I'm going to get destructive interference.

1301
01:27:27.259 --> 01:27:29.521
Which is at the boundary of the dark pink and the light pink.

1302
01:27:29.641 --> 01:27:30.281
Yeah.

1303
01:27:30.361 --> 01:27:31.102
In this visual here.

1304
01:27:31.142 --> 01:27:31.682
Yeah, yeah, yeah.

1305
01:27:31.843 --> 01:27:31.983
Yeah.

1306
01:27:32.143 --> 01:27:32.383
Okay.

1307
01:27:32.423 --> 01:27:32.923
Yeah.

1308
01:27:33.164 --> 01:27:37.968
So this is how the double slit experiment works for like light waves and things like that.

1309
01:27:38.428 --> 01:27:41.950
Now, crucially, it's been shown that single particles also do this, right?

1310
01:27:42.230 --> 01:27:56.918
I can make the light dim down to the point when only a single photon is going through, and the single photon, the wave function goes through both, and it interferes with itself to create single photon-like interference on my detector, right?

1311
01:27:57.718 --> 01:28:04.502
So, Feynman took a look at this, and he had a different way of explaining it.

1312
01:28:04.842 --> 01:28:06.022
Feynman had this idea of...

1313
01:28:07.862 --> 01:28:12.405
the path formulation, sum over all paths of quantum mechanics.

1314
01:28:12.986 --> 01:28:16.208
And he explained all of quantum mechanics using the sum over paths.

1315
01:28:16.348 --> 01:28:18.670
He didn't like the wave function analogy.

1316
01:28:18.770 --> 01:28:20.131
He came up with his own.

1317
01:28:20.451 --> 01:28:24.814
And it turns out that it's really good because it has applications to quantum field theory.

1318
01:28:25.194 --> 01:28:28.677
And if you know about Feynman diagrams, that's all the sum over paths stuff.

1319
01:28:29.197 --> 01:28:30.878
Okay, so here's how he explained it.

1320
01:28:31.359 --> 01:28:35.822
This is directly from one of his Feynman lectures of physics.

1321
01:28:36.883 --> 01:28:39.404
I've added the red lines and things like that.

1322
01:28:39.824 --> 01:28:42.104
So on the left, I've got an electron gun.

1323
01:28:42.204 --> 01:28:45.985
Again, I've got those two holes, and I've got a detector on that side.

1324
01:28:46.625 --> 01:28:47.265
Here's what he says.

1325
01:28:47.925 --> 01:28:59.748
He says, if I've got an electron gun, right, that's spitting out electrons, even if it's a single electron at a time, the electron is going to go... And suppose I put my detector at that bottom spot over there, okay?

1326
01:29:01.253 --> 01:29:06.838
The only thing I can do is calculate the probability that the detector is going to register an electron there.

1327
01:29:07.479 --> 01:29:09.721
And what I want to do is calculate what is that probability.

1328
01:29:10.101 --> 01:29:13.985
What's the probability that I'm going to see an electron here or here or here or anywhere else?

1329
01:29:14.766 --> 01:29:19.030
He said the electron is going to go through all of the paths.

1330
01:29:19.650 --> 01:29:23.494
And the way we're going to keep track of what the electron is doing is I'm going to assign...

1331
01:29:25.528 --> 01:29:27.849
I'm going to assign an arrow to that electron.

1332
01:29:28.309 --> 01:29:28.550
Okay?

1333
01:29:28.870 --> 01:29:32.472
The electron is going to start out from the gun with the arrow pointing to the right.

1334
01:29:33.492 --> 01:29:38.535
And as it moves along in the universe, the arrow is going to spin around like a clock.

1335
01:29:39.281 --> 01:29:43.522
And the frequency of that spinning has to do with the frequency of the electron's wave function.

1336
01:29:43.802 --> 01:29:49.003
For example, if this was a particle of light, the frequency would literally be the frequency of the light.

1337
01:29:49.023 --> 01:29:49.704
Okay?

1338
01:29:50.104 --> 01:29:56.565
But now imagine, I've got this electron that starts out with an arrow pointed to the right, and it's spinning and it's spinning.

1339
01:29:57.165 --> 01:30:02.907
It goes to the first slit at the top, slit number one, and it goes down to where the detector is at the bottom.

1340
01:30:03.347 --> 01:30:03.567
Okay?

1341
01:30:04.247 --> 01:30:13.551
As it's spinning, it's going to end up at the detector and the clock is going to be at a certain location on the 0 to 12.

1342
01:30:14.131 --> 01:30:15.711
It's going to be pointing in a certain direction.

1343
01:30:16.272 --> 01:30:16.912
And it spins.

1344
01:30:17.192 --> 01:30:20.393
Yeah, and it spins because it traveled for some amount of time.

1345
01:30:20.813 --> 01:30:24.895
And during that time, it made some amount of rotations based on its frequency.

1346
01:30:25.761 --> 01:30:26.001
Okay.

1347
01:30:26.481 --> 01:30:28.042
Now what about the second path?

1348
01:30:28.462 --> 01:30:30.563
The electron is going to go through every single path.

1349
01:30:30.943 --> 01:30:38.707
So if we look at what's going to happen at the second path, there's another path that the electron can take, let's say the blue path.

1350
01:30:39.067 --> 01:30:40.588
And the electron is going to spin again.

1351
01:30:40.628 --> 01:30:42.448
It's going to start out at the same part.

1352
01:30:42.949 --> 01:30:44.850
It's going to spin, and it's going to get to...

1353
01:30:45.950 --> 01:30:54.761
That same point, but it's going to be pointing in a different direction because the path length is different, which means the time is going to be different, which means the amount of time that it's been spinning is different.

1354
01:30:54.801 --> 01:30:58.145
So it's going to end up pointing in a different direction.

1355
01:30:58.605 --> 01:31:03.091
So he said, if we were to now calculate what is the probability of finding...

1356
01:31:04.567 --> 01:31:05.387
an electron there.

1357
01:31:05.808 --> 01:31:07.789
All I have to do is add up the two arrows.

1358
01:31:08.749 --> 01:31:11.291
So I add up the blue arrow and the red arrow, these two vectors.

1359
01:31:11.671 --> 01:31:14.012
I get a resultant arrow, which is the black thing.

1360
01:31:14.733 --> 01:31:19.976
And then I take the, the, the area of the circle that, that black arrow creates.

1361
01:31:19.996 --> 01:31:20.296
Um,

1362
01:31:20.456 --> 01:31:27.702
This is his version of Born's rule, which is that the square of the amplitude of the wave function tells you the probability.

1363
01:31:27.982 --> 01:31:29.883
He's saying, oh, just take an area of a circle.

1364
01:31:30.464 --> 01:31:33.826
He was a wizard with like creating mental models.

1365
01:31:33.906 --> 01:31:34.987
And this was his way of doing it.

1366
01:31:35.027 --> 01:31:37.429
So the area of that circle tells you the probability.

1367
01:31:37.569 --> 01:31:37.769
Right.

1368
01:31:37.989 --> 01:31:38.249
Okay?

1369
01:31:38.390 --> 01:31:38.590
Yes.

1370
01:31:38.750 --> 01:31:40.992
And that's the probability for that spot down there.

1371
01:31:41.172 --> 01:31:41.432
Mm-hmm.

1372
01:31:42.252 --> 01:31:46.075
And you could do this same thing for every spot along the detector.

1373
01:31:46.195 --> 01:31:46.555
Very good.

1374
01:31:46.815 --> 01:31:50.377
So now let's talk about what is the probability in the very middle?

1375
01:31:51.058 --> 01:31:54.460
Where in the very middle, the two paths are exactly equal.

1376
01:31:55.160 --> 01:32:04.126
And so the arrows for the two paths are going to point in the same direction, which is why the area of the circle is going to be way bigger.

1377
01:32:05.300 --> 01:32:12.004
And so now if you go to the next slide, you'll actually see that this corresponds to that interference pattern that we saw.

1378
01:32:12.365 --> 01:32:12.585
Right.

1379
01:32:12.905 --> 01:32:13.105
Right?

1380
01:32:13.365 --> 01:32:13.545
Right.

1381
01:32:13.645 --> 01:32:18.909
Where in the middle you have constructive interference because the two arrows are pointing in the same direction.

1382
01:32:19.029 --> 01:32:20.630
Having a larger area of probability.

1383
01:32:20.650 --> 01:32:20.790
Yeah.

1384
01:32:21.050 --> 01:32:30.717
But where the troughs are, where there's zero probability, that's because the timing there is just right where the arrows are opposite.

1385
01:32:30.737 --> 01:32:30.877
Mm-hmm.

1386
01:32:32.118 --> 01:32:33.599
Right?

1387
01:32:33.639 --> 01:32:39.043
The angles of their rotation at that particular spot happen to be effectively in opposite direction.

1388
01:32:39.083 --> 01:32:39.824
In opposite direction.

1389
01:32:39.864 --> 01:32:44.268
Which creates that thin line of demarcation where it's destructive.

1390
01:32:44.528 --> 01:32:44.968
Exactly.

1391
01:32:45.288 --> 01:32:49.972
And normally with undergrad physics, we think about like it's half a wavelength away.

1392
01:32:50.433 --> 01:32:54.596
But half a wavelength means that the clock has turned exactly 180 degrees and not 360 degrees.

1393
01:32:55.837 --> 01:33:01.060
And so this is his way of saying half a wavelength is really my arrow is pointing in the opposite direction.

1394
01:33:01.100 --> 01:33:01.740
That's interesting.

1395
01:33:02.100 --> 01:33:06.423
It's a different visual metaphor to explain the same idea.

1396
01:33:06.443 --> 01:33:07.943
Yes, but it's the same math, right?

1397
01:33:08.224 --> 01:33:14.747
And crucially here, what I want to point out is it doesn't matter which way the arrows point at the end.

1398
01:33:15.543 --> 01:33:15.823
Okay.

1399
01:33:16.423 --> 01:33:16.843
How do you mean?

1400
01:33:16.963 --> 01:33:23.646
What I mean is even if the top arrow, both of the arrows pointed in the opposite direction, the area of the circle would be the same.

1401
01:33:23.666 --> 01:33:24.846
The probability would still be the same.

1402
01:33:25.046 --> 01:33:29.568
You're saying so currently we're looking at both of the arrows pointing slightly, let's say, like northwest.

1403
01:33:29.588 --> 01:33:30.488
Sorry, excuse me, northeast.

1404
01:33:30.948 --> 01:33:36.291
If we flipped both of them 180 degrees, it doesn't impact the probability.

1405
01:33:36.311 --> 01:33:37.171
Yes, exactly.

1406
01:33:37.211 --> 01:33:37.932
It's the exact same.

1407
01:33:37.952 --> 01:33:42.634
What only matters is the relative between the angle between the two arrows.

1408
01:33:42.914 --> 01:33:48.257
As long as the two add up, the circle remains the same.

1409
01:33:48.517 --> 01:33:49.877
That's a little bit of a key here.

1410
01:33:50.678 --> 01:33:56.721
The probability space is the same independent of the direction of spin in this construction.

1411
01:33:57.721 --> 01:33:57.941
Yeah.

1412
01:33:58.882 --> 01:33:59.042
Yeah.

1413
01:33:59.672 --> 01:34:03.035
And independent of the direction of like which way the phase ends up.

1414
01:34:03.435 --> 01:34:04.396
Right, right, right.

1415
01:34:04.456 --> 01:34:05.517
Which way the phase ends up.

1416
01:34:05.577 --> 01:34:07.618
The spin is a loaded word.

1417
01:34:07.638 --> 01:34:08.199
It's a loaded word.

1418
01:34:08.239 --> 01:34:09.380
Okay, no, that's fair.

1419
01:34:09.440 --> 01:34:11.141
I want to be which way the phase ends up.

1420
01:34:11.161 --> 01:34:11.821
Yeah, understood.

1421
01:34:11.902 --> 01:34:12.102
Yeah.

1422
01:34:12.802 --> 01:34:13.503
Okay, so...

1423
01:34:15.464 --> 01:34:18.567
Yeah, that's the crucial thing to realize is the direction of the arrows don't matter.

1424
01:34:18.607 --> 01:34:21.730
It's only the relative directions relative to one another.

1425
01:34:21.950 --> 01:34:29.938
And so part of this is we started this conversation here because we were talking about this algorithm –

1426
01:34:31.019 --> 01:34:35.243
Where we were putting in the 0010111, right?

1427
01:34:36.284 --> 01:34:41.929
And we talked about this idea that it's a superposition state.

1428
01:34:42.229 --> 01:34:51.898
And so we have to put it – when we're talking about it as a quantum Turing machine, a quantum algorithm, we can't factor it like we would in a classical system.

1429
01:34:52.318 --> 01:34:56.082
And so we are able to basically have it either be balanced –

1430
01:34:56.602 --> 01:35:02.787
or constant, which gives us effectively this ability to have a zero or one in a quantum system.

1431
01:35:02.807 --> 01:35:08.791
That's what we talked about previously, just from a basic, from a math perspective.

1432
01:35:09.131 --> 01:35:17.537
The reason we brought up the double slit and this Feynman diagram concept is it's representing the same concept.

1433
01:35:18.618 --> 01:35:18.878
It is.

1434
01:35:19.178 --> 01:35:20.359
Go ahead.

1435
01:35:20.559 --> 01:35:22.521
In the sense that those arrows...

1436
01:35:22.721 --> 01:35:22.941
Yes.

1437
01:35:22.961 --> 01:35:23.221
Yes.

1438
01:35:24.060 --> 01:35:30.062
Those arrows represent the complex number that is in front of those states.

1439
01:35:30.282 --> 01:35:30.462
Right.

1440
01:35:30.482 --> 01:35:34.783
You know when I said like the 0, 0, the 0, 1, and like I put a minus 1?

1441
01:35:35.203 --> 01:35:36.083
That's what it represents.

1442
01:35:36.103 --> 01:35:38.524
So let's actually make a... Oh, sorry.

1443
01:35:38.544 --> 01:35:38.784
Go ahead.

1444
01:35:38.804 --> 01:35:39.264
No, go ahead.

1445
01:35:39.384 --> 01:35:40.004
Actually, yeah, no.

1446
01:35:40.064 --> 01:35:42.705
So I'm actually going to make a direct...

1447
01:35:43.005 --> 01:35:43.245
Okay.

1448
01:35:43.265 --> 01:35:47.528
Comparison between our Deutsch-Joseph algorithm and that quantum experiment.

1449
01:35:47.548 --> 01:35:47.708
Perfect.

1450
01:35:47.728 --> 01:35:51.131
And I think you'll see the reason why I sort of did that.

1451
01:35:51.171 --> 01:35:51.891
So actually, let's go.

1452
01:35:52.171 --> 01:35:53.252
So yeah, this is, yeah.

1453
01:35:53.272 --> 01:35:56.154
So if we want to review, this is the Deutsch-Joseph algorithm, right?

1454
01:35:56.214 --> 01:35:56.434
Yes.

1455
01:35:56.454 --> 01:35:59.356
You've got the 0, 0, 0, 0, 1, 1, 0, 1, 1, right?

1456
01:36:00.097 --> 01:36:03.079
It starts out with just a 1 in front of everything.

1457
01:36:03.499 --> 01:36:05.620
So it starts out with the arrows pointing to the right.

1458
01:36:06.161 --> 01:36:06.381
Okay?

1459
01:36:06.621 --> 01:36:09.323
And now it's going to go through the quantum apparatus and...

1460
01:36:09.643 --> 01:36:12.207
And the amplitudes are going to start rotating.

1461
01:36:13.028 --> 01:36:15.111
And what we want to do is have them interfere at the end.

1462
01:36:15.952 --> 01:36:21.140
So now, let's consider instead of two slits, four slits.

1463
01:36:22.267 --> 01:36:23.608
You see where this is going?

1464
01:36:24.008 --> 01:36:25.109
Yeah?

1465
01:36:25.189 --> 01:36:28.792
Our slits are the function in some sense, right?

1466
01:36:29.033 --> 01:36:31.555
And we've created a superposition.

1467
01:36:32.215 --> 01:36:36.078
Each of the superpositions is represented by the four holes, okay?

1468
01:36:36.319 --> 01:36:37.540
And I've got an electron gun.

1469
01:36:38.320 --> 01:36:46.447
This is, I think, how Feynman might have, like, if he was around to do science communication now, maybe this is how he would have done it, right?

1470
01:36:47.048 --> 01:36:47.288
So...

1471
01:36:48.432 --> 01:36:55.520
I've got my four holes, and those four holes represent the four binary digits that can go through.

1472
01:36:55.861 --> 01:36:56.121
Okay?

1473
01:36:56.641 --> 01:36:57.943
Now, let's see what happens.

1474
01:36:58.924 --> 01:37:05.111
The function itself is going to be implemented by some kind of crystal that I'm going to put in those holes.

1475
01:37:05.131 --> 01:37:05.491
Okay?

1476
01:37:05.912 --> 01:37:06.072
Okay.

1477
01:37:08.902 --> 01:37:14.186
And depending on where the crystals are, that's going to tell me which output goes to 1 and which output goes to 0.

1478
01:37:14.426 --> 01:37:16.687
It's the idea that the crystal refracts the light.

1479
01:37:16.727 --> 01:37:17.388
Yeah, yeah.

1480
01:37:17.428 --> 01:37:18.668
No, what it's going to do is flip.

1481
01:37:18.869 --> 01:37:19.109
Flip.

1482
01:37:19.149 --> 01:37:19.349
Got it.

1483
01:37:19.369 --> 01:37:19.569
Okay?

1484
01:37:19.829 --> 01:37:26.013
Whatever direction the arrow came in into that hole, it's just going to add a pi pulse.

1485
01:37:26.053 --> 01:37:27.514
It's going to add 180 degrees.

1486
01:37:27.554 --> 01:37:34.559
So in this case, this particular function, this iteration of the function, maps the first and the last function.

1487
01:37:34.923 --> 01:37:40.428
0, 0, and 1, 1 into 0, and 0, 1, and 1, 0 into 1.

1488
01:37:40.748 --> 01:37:43.110
So this is the XOR function that I'm looking at right now.

1489
01:37:43.130 --> 01:37:43.370
Got it.

1490
01:37:43.450 --> 01:37:54.540
The XOR function would have the two crystals that are doing the, I don't know, whatever type of crystal it is, but the two crystals are going to be in the second and the third slits because those are the ones that are getting mapped to 1, okay?

1491
01:37:54.840 --> 01:37:56.862
In this case, this is a balanced function, right?

1492
01:37:57.423 --> 01:37:59.565
And so that's where I would, but the point is,

1493
01:38:00.683 --> 01:38:04.812
Somebody put the slits there with the holes and put, we don't know where the holes are.

1494
01:38:04.912 --> 01:38:05.974
In this case, we do, right?

1495
01:38:06.415 --> 01:38:08.399
But now let's go to the next one.

1496
01:38:09.415 --> 01:38:20.107
Now, suppose that it is a constant, meaning either there's no crystals in either of the folds or there's crystals in all four of them.

1497
01:38:20.307 --> 01:38:20.528
Right.

1498
01:38:20.688 --> 01:38:20.968
Okay?

1499
01:38:21.308 --> 01:38:22.490
In that case, what would happen?

1500
01:38:22.810 --> 01:38:30.359
If there's nothing, then they would all take the red line and all four of the arrows would point in the same direction.

1501
01:38:30.379 --> 01:38:30.599
Mm-hmm.

1502
01:38:31.139 --> 01:38:32.901
because they're all constructively interfering.

1503
01:38:33.201 --> 01:38:34.362
This would be four pluses.

1504
01:38:34.482 --> 01:38:38.446
Yeah, this would be four pluses, and the resulting arrow would be really long.

1505
01:38:38.806 --> 01:38:51.899
On the other hand, if there's four crystals, then I'm going to add a 180, and so no matter where I ended up before, I have the 180 added by the crystal, and so they're all going to be pointing in the opposite direction.

1506
01:38:52.812 --> 01:38:57.916
The phase is going to be pointing in the opposite direction, but the circle that I make is going to be the same.

1507
01:38:57.936 --> 01:38:59.176
The area of probability is going to be the same.

1508
01:38:59.357 --> 01:38:59.537
Right?

1509
01:38:59.577 --> 01:39:01.438
So I will still detect a particle.

1510
01:39:02.098 --> 01:39:03.159
This is fascinating.

1511
01:39:03.399 --> 01:39:13.006
Again, in this constant function, whether either no crystals or all four crystals, our arrow length…

1512
01:39:14.286 --> 01:39:16.387
is the same but in opposite directions.

1513
01:39:16.407 --> 01:39:16.627
Yes.

1514
01:39:16.947 --> 01:39:19.868
But it doesn't matter in the context of the probabilities.

1515
01:39:19.908 --> 01:39:20.208
Yes.

1516
01:39:20.468 --> 01:39:27.750
Because in the Feynman construction, the area of the circle will be identical.

1517
01:39:27.871 --> 01:39:30.671
The phase direction is irrelevant in that context.

1518
01:39:30.691 --> 01:39:33.772
Yes, because the detector only cares about what is the area of the circle.

1519
01:39:33.792 --> 01:39:34.013
Yeah.

1520
01:39:34.133 --> 01:39:34.333
Right?

1521
01:39:34.353 --> 01:39:34.693
Yeah, yeah, yeah.

1522
01:39:34.733 --> 01:39:38.034
And so the detector is still going to register a bunch of electrons coming through.

1523
01:39:38.054 --> 01:39:38.354
Mm-hmm.

1524
01:39:38.714 --> 01:39:55.131
or a bunch of photons or whatever the thing and the idea is that because when it's constructive which is that center point which is a higher probability constructive interference that's why the area is so large and then when you get further to the

1525
01:39:56.833 --> 01:40:22.069
past the other side of these there's like a line of deconstructive interference yeah and then well i mean if i were to move the detector somewhere or the other then one of the path lengths will be different from the others right and so some of the arrows will be pointing this way but the other one that came here and traveled farther is going to like travel more and start like pointing in the other direction here in this case it's like it's like those two traveled at exactly the right amount to be

1526
01:40:22.627 --> 01:40:24.928
to be pointed in the same direction, right?

1527
01:40:24.968 --> 01:40:26.649
Now, so this is for a constant function.

1528
01:40:26.669 --> 01:40:28.509
Now let's look at what a balanced function would do.

1529
01:40:28.830 --> 01:40:29.550
Like the XOR.

1530
01:40:30.610 --> 01:40:42.495
In the XOR, the top two are going to have arrows pointing in one direction, but because the middle two have the crystals, they're going to add a phase factor, and so they're going to have arrows pointing in the opposite direction.

1531
01:40:42.535 --> 01:40:48.958
And so I'm going to get destructive interference in the middle, where I once had constructive, if there was all crystals or no crystals.

1532
01:40:48.998 --> 01:40:49.218
Yes.

1533
01:40:49.558 --> 01:40:49.738
Right?

1534
01:40:50.078 --> 01:40:51.999
So if I put a detector in the middle there,

1535
01:40:54.178 --> 01:40:56.040
And all I do is have a one-shot.

1536
01:40:56.341 --> 01:41:01.687
I do a one-shot, and I see, do I see a particle or not?

1537
01:41:02.588 --> 01:41:02.828
Right?

1538
01:41:04.070 --> 01:41:09.437
That'll tell me exactly what the crystal can, like, what type of filter...

1539
01:41:10.595 --> 01:41:33.926
the person is put is it a balanced filter with only two or is it a or is it a um a constant crucially it doesn't matter where i put these crystals as long as there's two yeah right as long as there's two two of the green arrows are gonna two of the arrows are gonna be pointing in the opposite direction because i've made that sign flip because the phase again doesn't matter

1540
01:41:34.106 --> 01:41:35.087
Yeah.

1541
01:41:35.147 --> 01:41:42.193
Like, if I were to put the crystal on the top one, then one of the bottom arrows, one of the bottom red arrows would flip.

1542
01:41:42.293 --> 01:41:42.593
Yeah, yeah.

1543
01:41:42.653 --> 01:41:44.334
And one of the top green arrows would flip.

1544
01:41:44.534 --> 01:41:46.856
But at the end of the day, the sum of the two would still be zero.

1545
01:41:47.036 --> 01:41:48.598
Yeah, yeah.

1546
01:41:48.838 --> 01:41:49.699
This is so good.

1547
01:41:49.999 --> 01:42:02.509
And this is so good because it goes back to what it makes me think of again, and correct me if I'm thinking about it, this gives this idea of that reversible function concept we talked about at the beginning.

1548
01:42:02.529 --> 01:42:02.669
Right.

1549
01:42:02.869 --> 01:42:03.069
Right.

1550
01:42:03.169 --> 01:42:16.657
Like we're able to take the result, the arrows on the right, and then look back to construct what the crystal construction was in the middle because we are able to look at the – or am I mixing metaphors there?

1551
01:42:16.677 --> 01:42:17.778
I think you're mixing metaphors there.

1552
01:42:17.818 --> 01:42:18.758
I'm mixing metaphors there.

1553
01:42:18.778 --> 01:42:19.819
Yeah, yeah, yeah.

1554
01:42:19.839 --> 01:42:20.019
Yeah.

1555
01:42:20.039 --> 01:42:23.181
The reversible part of stuff is happening like –

1556
01:42:24.101 --> 01:42:27.885
When we implement the function itself, like the reversible part is happening.

1557
01:42:28.305 --> 01:42:35.211
And that's when we have to get into the weeds about like how we actually implement this like function in a quantum computer.

1558
01:42:35.372 --> 01:42:36.873
We can plus.

1559
01:42:36.913 --> 01:42:39.796
Yeah, we need like an ancillary bit.

1560
01:42:40.396 --> 01:42:41.758
I think it's called an ancilla bit.

1561
01:42:42.318 --> 01:42:46.203
that like keeps track of all of the information that stuff here.

1562
01:42:46.263 --> 01:42:50.107
It's still, it's still, you're still losing information though here, right?

1563
01:42:50.408 --> 01:42:54.512
Because there's four inputs coming in and only one thing that I'm thinking.

1564
01:42:54.532 --> 01:42:55.153
Like, I got you.

1565
01:42:55.233 --> 01:42:55.433
Yes.

1566
01:42:55.574 --> 01:42:56.294
No, no, that makes sense.

1567
01:42:56.395 --> 01:42:56.715
I got you.

1568
01:42:56.735 --> 01:42:57.055
Yeah.

1569
01:42:57.075 --> 01:42:59.698
And like, remember quantum mechanics,

1570
01:43:00.604 --> 01:43:05.108
the observation is not reversible.

1571
01:43:05.169 --> 01:43:08.131
It destroys whatever thing is happening in the magic box.

1572
01:43:08.171 --> 01:43:08.452
Yes.

1573
01:43:08.692 --> 01:43:08.872
Right.

1574
01:43:08.912 --> 01:43:10.454
And here we're doing an observation.

1575
01:43:10.654 --> 01:43:10.834
Yeah.

1576
01:43:10.954 --> 01:43:13.917
And so that is definitely not reversible.

1577
01:43:13.957 --> 01:43:14.338
That's right.

1578
01:43:14.418 --> 01:43:14.578
Right.

1579
01:43:14.598 --> 01:43:14.978
That's right.

1580
01:43:14.998 --> 01:43:15.459
Yeah.

1581
01:43:15.479 --> 01:43:19.623
Whatever is, is the reversible parts happening before we make the observation.

1582
01:43:19.683 --> 01:43:19.923
Yeah.

1583
01:43:19.963 --> 01:43:20.183
Yeah.

1584
01:43:20.283 --> 01:43:23.967
The reversible part is how we implement whatever the Oracle and like,

1585
01:43:24.227 --> 01:43:28.390
How we create superpositions, because like we're going to start with zero, zero, zero, zero.

1586
01:43:28.630 --> 01:43:35.394
And then what you do is apply like a Hadamard gate that will make, OK, now I put in a superposition of zero and one, zero and one, zero and one.

1587
01:43:35.794 --> 01:43:37.155
And then I entangle them.

1588
01:43:37.175 --> 01:43:39.016
So now I get all of the different products.

1589
01:43:39.376 --> 01:43:42.918
So you can imagine for like N different binary digits, right?

1590
01:43:43.418 --> 01:43:46.360
This is going to scale like crazy for a classical computer.

1591
01:43:46.656 --> 01:43:49.141
But for a quantum computer, all I have to do is one shot.

1592
01:43:49.341 --> 01:43:53.188
It's what happens inside the brackets of the equation that we were looking at earlier.

1593
01:43:53.248 --> 01:43:57.717
Yeah, it happens inside of the... You start the qubits, then you do all the nonsense.

1594
01:43:57.817 --> 01:43:58.819
All of the nonsense...

1595
01:43:59.528 --> 01:44:00.589
It has to be reversible.

1596
01:44:00.849 --> 01:44:01.390
Right, right.

1597
01:44:01.430 --> 01:44:04.212
Before we make the observation at the very end.

1598
01:44:04.312 --> 01:44:05.273
No, that makes sense.

1599
01:44:05.373 --> 01:44:09.196
And that's a good distinction because there's just so many levels to this.

1600
01:44:09.236 --> 01:44:10.497
So thank you for that correction.

1601
01:44:10.737 --> 01:44:19.465
And so I'm just trying to make sure I'm tracking, connecting the ideas we built at the beginning and bringing them down now into reality.

1602
01:44:19.885 --> 01:44:41.982
But I think the way you explain this is between looking at the math structure of balanced versus constant and then correlating it to the experimental architecture of the double slit experiment as a way to visualize the idea of what we're trying to say is happening in the magic box.

1603
01:44:42.142 --> 01:44:43.203
Yeah, yeah.

1604
01:44:43.343 --> 01:44:47.065
The double slit experiment is kind of showing you this interference stuff, right?

1605
01:44:47.306 --> 01:44:47.866
Right, right.

1606
01:44:49.267 --> 01:44:51.249
Of course, it's a lot more complicated, right?

1607
01:44:51.669 --> 01:44:59.835
But the main point that I want to say is the reason why the Deutz-Joseph algorithm works is because it uses interference.

1608
01:45:00.576 --> 01:45:01.537
Okay?

1609
01:45:01.777 --> 01:45:06.921
It's like the problem itself is this kind of useless problem.

1610
01:45:07.429 --> 01:45:10.411
of like, oh, there's a function that's either balanced or constant.

1611
01:45:10.712 --> 01:45:11.552
Find out what it is.

1612
01:45:12.073 --> 01:45:19.538
And because it's contrived that way, we can use quantum mechanics to figure it out.

1613
01:45:20.319 --> 01:45:27.344
And part of the reason why this was the first algorithm is because it's designed to use quantum interference.

1614
01:45:27.364 --> 01:45:31.447
Deutsch was literally thinking about, how do I prove to these people that,

1615
01:45:31.647 --> 01:45:34.168
That there is a problem that exists, right?

1616
01:45:34.188 --> 01:45:42.771
A computational problem that I could solve with a quantum computer in a one shot that would require a classical computer an exponential amount of time.

1617
01:45:42.811 --> 01:45:45.752
This is a perfectly valid problem, right?

1618
01:45:46.092 --> 01:45:47.993
Why you would want to solve it, who knows?

1619
01:45:48.173 --> 01:45:50.254
Other than it's a very good mental exercise.

1620
01:45:50.274 --> 01:45:57.056
And it actually proved to the world that, okay, there is a computational problem out there.

1621
01:45:58.250 --> 01:46:01.591
that definitely a classical computer cannot solve.

1622
01:46:02.532 --> 01:46:02.752
Okay.

1623
01:46:02.812 --> 01:46:13.896
Which then created sort of this theoretical motivation or justification to say, okay, well, this is a problem that requires quantum computing to actually be able to efficiently solve.

1624
01:46:14.357 --> 01:46:17.338
And it's concrete.

1625
01:46:17.398 --> 01:46:18.298
It's right there.

1626
01:46:18.338 --> 01:46:18.798
It's right there.

1627
01:46:18.818 --> 01:46:18.958
Right.

1628
01:46:19.038 --> 01:46:19.639
It's right there.

1629
01:46:19.699 --> 01:46:20.979
I can describe it really well.

1630
01:46:21.039 --> 01:46:21.359
Yeah.

1631
01:46:21.399 --> 01:46:21.559
Right.

1632
01:46:21.840 --> 01:46:25.201
Still, I mean, obviously people are going to look at this and be like, well, that's a useless problem.

1633
01:46:25.321 --> 01:46:25.481
Yeah.

1634
01:46:25.561 --> 01:46:25.801
Okay.

1635
01:46:26.182 --> 01:46:29.004
Now we're going to get into some useful problems.

1636
01:46:29.404 --> 01:46:33.687
This is what we just connected back to the idea of funding and basic research.

1637
01:46:33.747 --> 01:46:36.229
Sometimes you got to do stuff that looks useless.

1638
01:46:36.409 --> 01:46:36.649
Yes.

1639
01:46:37.049 --> 01:46:40.972
In order to enable and create the foundation for things that are useful.

1640
01:46:41.032 --> 01:46:42.993
And it's so can be counterintuitive.

1641
01:46:43.213 --> 01:46:47.556
But I always want to hammer this point because we need to just explore sometimes.

1642
01:46:47.616 --> 01:46:48.517
Yes, I agree.

1643
01:46:48.677 --> 01:46:50.098
And just fool around.

1644
01:46:50.298 --> 01:46:51.218
and argue.

1645
01:46:52.219 --> 01:46:53.899
100%.

1646
01:46:54.259 --> 01:46:59.001
So, Doge Joza, they proposed this thing.

1647
01:46:59.041 --> 01:47:16.366
1993, computer scientist Daniel Simon, he formulates a quantum algorithm that demonstrates exponential speed-up over classical randomized algorithms where he's trying to consider a function that's guaranteed to have a hidden period under bitwise XOR addition.

1648
01:47:18.006 --> 01:47:19.327
I don't really want to get into it,

1649
01:47:20.235 --> 01:47:23.637
Effectively, there's a function that has some kind of period.

1650
01:47:23.697 --> 01:47:32.502
In this case, this is a function that maps three-digit binary numbers to other three-digit binary numbers, except there's...

1651
01:47:34.103 --> 01:47:35.964
two inputs always map to one input.

1652
01:47:36.044 --> 01:47:36.324
Okay?

1653
01:47:36.624 --> 01:47:40.146
So there's eight different binary numbers, but there's only four different outputs.

1654
01:47:40.506 --> 01:47:48.191
And like the two green inputs map to the same 101, 101, and the two red outputs map to the same 000, right?

1655
01:47:48.651 --> 01:47:50.752
And it turns out the bitwise XOR,

1656
01:47:51.412 --> 01:47:53.394
of the inputs is the same.

1657
01:47:53.614 --> 01:47:59.298
It's 110110 for both, if you were to take the bitwise XOR of both of the inputs.

1658
01:47:59.518 --> 01:48:08.845
The idea is, given I have a function like this, with this constraint, can you figure out what is that invariant bitwise XOR for the two matched

1659
01:48:09.405 --> 01:48:11.468
This is another contrived problem.

1660
01:48:11.588 --> 01:48:12.409
It's very similar.

1661
01:48:12.469 --> 01:48:20.460
It has a similar construction, but it creates a bit more complicated, creates a different mapping that ultimately is trying to accomplish the same concept.

1662
01:48:20.580 --> 01:48:20.800
Yeah.

1663
01:48:20.880 --> 01:48:26.607
It's like we're now trying to think of problems that a quantum computer could do very, very fast.

1664
01:48:27.128 --> 01:48:29.209
That a classical computer can't do very, very fast.

1665
01:48:29.289 --> 01:48:30.630
It's okay if you didn't understand that.

1666
01:48:31.351 --> 01:48:37.094
The idea is there's some type of period in my function, and this thing is trying to figure out what that period is.

1667
01:48:37.535 --> 01:48:37.775
Okay?

1668
01:48:38.495 --> 01:48:44.379
Simon submits his findings to the 1993 IEEE Symposium on Theory of Computing.

1669
01:48:44.499 --> 01:48:44.739
Okay?

1670
01:48:45.059 --> 01:48:47.161
And the program committee rejects the paper.

1671
01:48:47.181 --> 01:48:47.701
Okay.

1672
01:48:47.981 --> 01:48:52.704
Because it dismisses it as just another artificial black box puzzle.

1673
01:48:52.845 --> 01:48:54.846
It's like, oh, we got another Deutsch-Joseh here.

1674
01:48:55.406 --> 01:48:56.607
It's like, who cares?

1675
01:48:57.448 --> 01:49:03.372
When would I encounter such a periodic bitwise XOR addition function?

1676
01:49:04.132 --> 01:49:07.615
Mathematician Peter Schor is on the committee for the STOC.

1677
01:49:07.875 --> 01:49:10.457
This is Peter Schor when he was a young man.

1678
01:49:11.578 --> 01:49:16.962
And Schor advocates to accept that manuscript because he recognizes that this formulation...

1679
01:49:17.782 --> 01:49:22.084
represents a period finding over an algebraic group.

1680
01:49:22.584 --> 01:49:22.824
Okay.

1681
01:49:22.864 --> 01:49:23.164
Okay?

1682
01:49:24.264 --> 01:49:25.205
Why is this important?

1683
01:49:25.325 --> 01:49:40.850
He realizes that if period finding can be mapped to something that a quantum computer can do, period finding can also be mapped to cyclic groups over integers, okay?

1684
01:49:42.030 --> 01:49:50.145
meaning like there's some weird algebraic math over integers, and that can be applied to computational problems in cryptography.

1685
01:49:51.487 --> 01:49:53.751
The idea is the construction of this...

1686
01:49:54.948 --> 01:50:02.232
Has a functional application to cryptography because of some of the mathematical underpinnings.

1687
01:50:02.272 --> 01:50:02.512
Yes.

1688
01:50:03.212 --> 01:50:04.813
That define the problem.

1689
01:50:05.073 --> 01:50:05.514
Exactly.

1690
01:50:05.874 --> 01:50:13.098
And, you know, Peter Short, he looked at it and was able to see those mathematical underpinnings in the construction of...

1691
01:50:13.741 --> 01:50:15.682
Yeah, of the Simon problem, right?

1692
01:50:15.822 --> 01:50:16.703
Of Simon's problem.

1693
01:50:16.763 --> 01:50:25.188
He looked at this and he's like, this looks useless, but there's a way that this can be used to solve something that I think a lot of people are going to care about.

1694
01:50:25.448 --> 01:50:25.749
Okay?

1695
01:50:26.029 --> 01:50:30.512
So he sets out to extend Simon's technique to something called the discrete logarithm problem.

1696
01:50:31.032 --> 01:50:32.673
April 1994, he succeeds.

1697
01:50:33.233 --> 01:50:38.717
He figures out how to effectively do like a discrete Fourier transform.

1698
01:50:38.897 --> 01:50:40.118
You know, in Fourier transforms...

1699
01:50:40.838 --> 01:50:42.159
We've discussed this a lot for you.

1700
01:50:42.179 --> 01:50:50.606
Transforms are when you go from the time domain of a signal to the frequency domain where you're extracting the frequencies that are relevant in whatever thing, right?

1701
01:50:50.666 --> 01:50:55.150
In this case, this is like a frequency of numbers type thing, right?

1702
01:50:56.410 --> 01:50:58.791
And he shares this logarithm result at Bell Labs.

1703
01:50:58.811 --> 01:51:00.331
He was at Bell Labs.

1704
01:51:00.431 --> 01:51:02.792
Every Tuesday they used to have this weekly seminar.

1705
01:51:03.192 --> 01:51:04.572
He presents it at the seminar.

1706
01:51:05.593 --> 01:51:08.394
It's known for rigorous and direct questioning.

1707
01:51:08.994 --> 01:51:10.834
The presentation is very well received.

1708
01:51:11.634 --> 01:51:13.295
And over the following days...

1709
01:51:14.345 --> 01:51:17.969
everyone kind of realizes what Shore's going for, okay?

1710
01:51:18.729 --> 01:51:29.219
Shore's technique to the discrete logarithm problem gets out, and he starts getting phone calls from the academic community, because now it's spreading, okay?

1711
01:51:29.239 --> 01:51:32.903
Bell Labs had this seminar, the people who attended the seminar...

1712
01:51:33.236 --> 01:51:35.417
are talking to their friends, they're talking to their friends.

1713
01:51:36.878 --> 01:51:49.044
Through the grapevine, Umesh Vazirani, he's another computer scientist who currently is at the University of California, Berkeley, he phones Peter Shore on the weekend.

1714
01:51:49.064 --> 01:51:51.606
So Tuesday is when he gave the seminar, on the weekend...

1715
01:51:52.706 --> 01:52:17.293
uh vazarani phones got that phone call yeah he got that phone call and vazarani understands exactly where this is going and on the phone call he says i hear that you can factor efficiently with a quantum computer right and peter shore immediately is like this guy yeah he's got like he all he immediately like saw the through line right right in those four days though peter shore spent all

1716
01:52:22.583 --> 01:52:44.650
because basically he sort of had an incomplete map yeah and he had an inkling that this could probably work and now he got feedback that it could probably work more importantly he got feedback from people who could definitely make it work right and he's like i need to lock in yeah like this is my thing right i mean he uh peter short gave a gave a presentation at ucla like two or three years ago um

1717
01:52:45.910 --> 01:53:12.646
like a symposium and he was literally talking about this and he said you know when vazirani telephoned him and it's like i hear you can factor efficiently you know with a quantum computer he was like i had been working for four days and fortunately i had figured out how to do that if i hadn't and like i got that phone call i would have panicked because i'm like okay so now literally everybody is going after the factoring algorithm right that he is now known for peter shore

1718
01:53:14.293 --> 01:53:24.640
spends these days creating that, he establishes a way to find prime factors of large products of primes.

1719
01:53:25.420 --> 01:53:26.401
Why is that important?

1720
01:53:26.781 --> 01:53:38.929
Because almost all of cryptography is dependent on large products of primes not being able to get factored efficiently, even by a supercomputer.

1721
01:53:39.449 --> 01:53:39.729
Okay?

1722
01:53:40.009 --> 01:53:43.712
If you take a giant prime number and you take a giant prime number,

1723
01:53:44.678 --> 01:53:46.289
you get an even bigger number

1724
01:53:47.378 --> 01:53:53.563
And if you give that to somebody, they could not tell you what two prime numbers make up that product.

1725
01:53:53.903 --> 01:53:54.164
Okay?

1726
01:53:54.464 --> 01:53:55.465
Unless you give them one of them.

1727
01:53:55.485 --> 01:53:58.267
If you give them one of them, then you can just divide and I can get the other one.

1728
01:53:58.327 --> 01:53:58.487
Right?

1729
01:53:58.767 --> 01:54:02.931
This is how public key and private key encryption works.

1730
01:54:03.331 --> 01:54:05.533
Public key is the giant big number.

1731
01:54:05.973 --> 01:54:12.358
Private key is your own special prime number that you can figure out what the other one is based on just dividing.

1732
01:54:12.458 --> 01:54:14.620
And then you can, you know, this is how passwords work.

1733
01:54:14.700 --> 01:54:15.521
Email passwords.

1734
01:54:15.781 --> 01:54:17.123
your Instagram password.

1735
01:54:17.463 --> 01:54:23.969
This is why like hackers need to like fool you by telling you that like, you know, your, your grandma's in the hospital or something.

1736
01:54:24.350 --> 01:54:24.990
Yeah.

1737
01:54:25.010 --> 01:54:27.173
And they actually literally need you to type in your past.

1738
01:54:27.213 --> 01:54:28.234
They can't just like do it.

1739
01:54:28.374 --> 01:54:28.654
Yeah.

1740
01:54:28.754 --> 01:54:28.934
Right.

1741
01:54:29.695 --> 01:54:31.637
This becomes a huge, huge deal.

1742
01:54:32.178 --> 01:54:32.878
Okay.

1743
01:54:32.978 --> 01:54:35.541
In parallel, I just want to also mention in 1996, love Grover,

1744
01:54:37.703 --> 01:54:39.464
who's actually, he's an Indian.

1745
01:54:40.444 --> 01:54:42.785
He develops Grover algorithm also at Bell Labs.

1746
01:54:43.205 --> 01:54:45.346
And this is another foundational quantum algorithm.

1747
01:54:45.386 --> 01:54:49.248
It's the second big foundational quantum algorithm that people are excited about.

1748
01:54:49.508 --> 01:54:50.449
It's optimal...

1749
01:54:51.596 --> 01:55:12.152
searching of an unstructured database so if you want to find like where something is you can do it in square root of n time instead of like n and would be you know you got to check every single one to figure out where it is square root of n is what he showed so this is also this can be like you know applied to a various other things these are the two big algorithms that

1750
01:55:12.412 --> 01:55:21.295
that are the reason why I think quantum computing has found all of this funding specifically, I think shorts and be perfectly honest.

1751
01:55:21.475 --> 01:55:28.096
They're, they sort of have two fundamental entry points of what they're actually either doing or solving for.

1752
01:55:28.697 --> 01:55:31.958
One is this sort of large factoring, large primes.

1753
01:55:32.578 --> 01:55:38.900
And the other is like, uh, unlike some unbounded database search or bounded database search.

1754
01:55:39.140 --> 01:55:39.360
Yeah.

1755
01:55:39.740 --> 01:55:40.500
Um, and yeah,

1756
01:55:42.061 --> 01:55:49.803
because of the structure of the problem, they fundamentally approach it in different ways.

1757
01:55:49.883 --> 01:55:53.823
And so there's implications and derivative effects.

1758
01:55:53.883 --> 01:55:57.804
Yeah, you can map certain problems to database search.

1759
01:55:58.004 --> 01:55:58.224
Right.

1760
01:55:58.284 --> 01:56:00.365
And then be like, oh, just apply Grover's algorithm.

1761
01:56:00.405 --> 01:56:00.605
Right.

1762
01:56:00.725 --> 01:56:07.286
I don't know if there's a lot that you can map to Shor's algorithm, but you don't need mapping to understand why Shor's is good.

1763
01:56:07.986 --> 01:56:11.287
Shor is just like, look, literally anyone in cryptography...

1764
01:56:12.277 --> 01:56:22.545
CIA, NSA, FBI, China, France, any intelligence community is going to want to have their access to something that can do shores.

1765
01:56:22.605 --> 01:56:28.229
World wars have been lost over not being able to encrypt your communications.

1766
01:56:28.309 --> 01:56:28.789
100%.

1767
01:56:28.869 --> 01:56:30.391
And so from the – Good point.

1768
01:56:30.471 --> 01:56:31.872
You know, like that is the –

1769
01:56:32.372 --> 01:56:33.312
Yeah, exactly.

1770
01:56:33.592 --> 01:56:39.594
And prior to Shor's 1994 factoring paper, quantum computing research was confined to academic communities.

1771
01:56:40.094 --> 01:56:47.116
IBM, Yorktown Heights, Oxford, Los Alamos, Bell Labs, physics departments, computer science departments.

1772
01:56:47.737 --> 01:56:50.497
Shor's algorithm altered that dynamic, right?

1773
01:56:50.897 --> 01:56:54.439
Because now it introduced national security, cryptography.

1774
01:56:54.959 --> 01:56:55.299
Yeah.

1775
01:56:56.339 --> 01:57:13.298
If you have an operational quantum processor that could scale to several thousand logical qubits, now any encrypted communication that relies on RSA, the elliptic curve cryptography that is the bedrock of Bitcoin's blockchain,

1776
01:57:13.979 --> 01:57:15.040
You can now decrypt it.

1777
01:57:15.240 --> 01:57:16.701
I can steal all your Bitcoin.

1778
01:57:17.582 --> 01:57:20.885
There's, like, dude, it's kind of scary because, like, I've been reading.

1779
01:57:21.265 --> 01:57:32.635
There's, I don't know what you want to call them, cyberpunk, cyber gangs, cyber terrorists even, that are just, like, downloading data.

1780
01:57:32.875 --> 01:57:33.055
Mm-hmm.

1781
01:57:33.985 --> 01:57:41.131
So that one day when there's a – they're just waiting for one day there's going to be a fault-tolerant quantum computer and then I can just decrypt it.

1782
01:57:41.252 --> 01:57:44.975
It's that HGTV show or whatever, Lifetime TV show, Hoarders.

1783
01:57:45.876 --> 01:57:45.976
Oh.

1784
01:57:46.096 --> 01:57:46.396
Right?

1785
01:57:46.436 --> 01:57:47.057
Yeah, yeah, yeah.

1786
01:57:47.077 --> 01:57:49.519
They just take whatever – They're just hoarding data.

1787
01:57:49.959 --> 01:57:50.159
Right.

1788
01:57:50.199 --> 01:57:50.400
Yeah.

1789
01:57:50.660 --> 01:57:55.064
And this is such – I just briefly want to note that this is kind of like the –

1790
01:57:56.194 --> 01:58:01.257
the scare tactic that in the media context is thrown around a lot.

1791
01:58:01.317 --> 01:58:11.483
It's like, oh, well, like everything that you think is secure now, like don't put anything on the internet because as soon as you have something that breaks this encryption, then all of your stuff is accessible.

1792
01:58:11.883 --> 01:58:15.305
And it, again, like most things, somewhere in the middle.

1793
01:58:15.405 --> 01:58:23.510
It's somewhere in the middle because like, yes, if you rely on the old algorithms for too long and then a fault-tolerant quantum computer comes in,

1794
01:58:24.614 --> 01:58:25.435
It's going to be an issue.

1795
01:58:25.535 --> 01:58:31.701
On the other hand, there's concerns about – there's people that calculate how long is it going to take.

1796
01:58:31.881 --> 01:58:32.962
Okay, it's fine.

1797
01:58:33.002 --> 01:58:34.643
It's not going to take the age of the universe.

1798
01:58:35.044 --> 01:58:39.688
But for certain hardware implementations, it might take days or weeks or months.

1799
01:58:40.648 --> 01:58:43.010
I mean, okay, that's better than the age of the universe.

1800
01:58:43.410 --> 01:58:49.954
But maybe, given how expensive quantum computers are going to be, maybe they're not going to want to get to your Instagram.

1801
01:58:50.214 --> 01:58:51.715
Maybe your Instagram is not worth that.

1802
01:58:52.195 --> 01:58:57.799
On the other hand, there are also ways to go post-quantum cryptography.

1803
01:58:57.819 --> 01:58:59.480
There are protocols that are in place.

1804
01:58:59.760 --> 01:59:07.305
And I think the U.S. government and DARPA specifically have, and I think NIST, the National Institute for Standards and Technology, they've created like...

1805
01:59:08.285 --> 01:59:18.554
sort of mission statements on how do we go into a post-quantum cryptography world where things can't be hacked by a quantum computer.

1806
01:59:18.754 --> 01:59:20.276
So there are efforts to do this.

1807
01:59:20.416 --> 01:59:23.178
It's still kind of an issue, right?

1808
01:59:23.238 --> 01:59:33.607
Because if adversarial nation states like China, I think we have a headline from Bloomberg that says that China is closing the gap in quantum technology.

1809
01:59:33.934 --> 01:59:38.299
This is a concern for our own State Department and the State Departments of the West, right?

1810
01:59:38.340 --> 01:59:47.291
Because clearly, I mean, you know, for whatever reason geopolitical, China is an adversarial nation.

1811
01:59:47.791 --> 01:59:51.356
And so if they get to this before we do, that's going to be an issue.

1812
01:59:52.227 --> 01:59:57.973
Critical infrastructure is definitely going to be the frontier of this battle.

1813
01:59:58.234 --> 01:59:58.454
Yeah.

1814
01:59:58.894 --> 02:00:05.742
And because people are going to want to use it for both defensive but 100% offensive purposes.

1815
02:00:05.782 --> 02:00:06.403
Because in any...

1816
02:00:08.607 --> 02:00:13.992
proxy war or other kind of geopolitical conflict between the superpowers.

1817
02:00:15.613 --> 02:00:19.937
This is a thumb on the scale that can be pressed immediately.

1818
02:00:20.137 --> 02:00:26.783
That arguably because of how connected we are digitally across the world now and even a lot of –

1819
02:00:27.703 --> 02:00:49.238
systems you can air gap stuff and etc but even we've seen the example of like stuxnet with the iranian nuclear missile program and how we can find ways into these systems that ostensibly are not connected to the quote-unquote internet yeah and still have a lot of damage and so this is i know the focus of

1820
02:00:50.533 --> 02:00:57.461
Thousands, tens of thousands of people every single day in a variety of ways.

1821
02:00:58.722 --> 02:01:05.110
Because the implications are you would not want encrypted systems related to missiles, silos.

1822
02:01:05.130 --> 02:01:06.091
Yeah, that would be really bad.

1823
02:01:06.131 --> 02:01:07.392
And other kind of things.

1824
02:01:07.913 --> 02:01:10.336
You would not want that to be easily accessible.

1825
02:01:10.356 --> 02:01:10.456
Yeah.

1826
02:01:10.516 --> 02:01:11.356
Yes, exactly.

1827
02:01:11.396 --> 02:01:12.076
As an example.

1828
02:01:12.196 --> 02:01:12.396
Yeah.

1829
02:01:12.677 --> 02:01:18.918
And to show you just how much Shor's algorithm really changed the landscape, Shor's algorithm came out in the 1990s.

1830
02:01:19.338 --> 02:01:31.961
And the DARPA QIST program established in 2001, this is the Quantum Information Science and Technology Initiative, this is the thing that funded university and industrial laboratories to pursue scalable qubit hardware.

1831
02:01:32.661 --> 02:01:37.842
This created the funding that enabled now technologies like companies

1832
02:01:40.523 --> 02:01:46.347
places to now piggyback off that research and try to create an actual quantum computer.

1833
02:01:46.387 --> 02:01:51.730
The ARDA roadmap, the A-R-D-A, that's the advanced research and development activity.

1834
02:01:53.251 --> 02:02:07.600
In 2002 and 2004, they convened like a quantum information science and technology experts panel to draft formal roadmaps to establish benchmarks on things like how good a quantum computer works,

1835
02:02:08.160 --> 02:02:15.404
can keep its quantum superpositions, things like gate fidelity, qubit scalability, and quantum error correction.

1836
02:02:15.745 --> 02:02:21.028
Those are more hardware questions, which we're going to get into in the next episode when we talk about the hardware.

1837
02:02:21.328 --> 02:02:30.093
But I hope that this episode kind of showed you, you know, kind of the theory behind it and why we're building this thing in the first place.

1838
02:02:30.433 --> 02:02:30.713
Okay.

1839
02:02:31.054 --> 02:02:36.417
And I really personally, I think it's personally, I think it's because of Shores and Grover's.

1840
02:02:37.037 --> 02:02:46.809
Feynman's dream of material science, I think in the age of AI, it's less so much a priority, right?

1841
02:02:46.869 --> 02:02:51.955
Because just look at Google DeepMind's Alpha Fold.

1842
02:02:52.734 --> 02:02:57.376
It won the Nobel Prize because it's really that good at predicting protein structure.

1843
02:02:57.997 --> 02:03:01.398
Maybe we don't need a quantum computer to predict protein structure.

1844
02:03:01.659 --> 02:03:02.819
I will make a small note.

1845
02:03:03.179 --> 02:03:05.581
Yes, it's not 100% efficient.

1846
02:03:06.061 --> 02:03:12.244
Yes, we've gotten a lot of comments about, yes, alpha-fold is interesting, but when brought into later stages...

1847
02:03:12.784 --> 02:03:14.245
So I'm just qualifying it.

1848
02:03:14.625 --> 02:03:16.066
Yes, we are aware.

1849
02:03:16.666 --> 02:03:17.667
It's not perfect.

1850
02:03:17.707 --> 02:03:19.668
We're not saying that it's perfect.

1851
02:03:19.688 --> 02:03:26.592
But from where we were before to it existing and being able to then iterate and build on top of that.

1852
02:03:27.192 --> 02:03:27.892
It's going to get good.

1853
02:03:28.012 --> 02:03:34.436
And there's no reason to believe that it's not going to get good for material science itself and physics in general.

1854
02:03:35.436 --> 02:03:36.257
The other thing why –

1855
02:03:37.117 --> 02:03:51.450
The other reason is like, I think the best algorithm that's out there to, the one that's like most frequently used to figure out things like ground states of a material is something called the variational quantum eigensolver.

1856
02:03:52.131 --> 02:04:01.773
This is, you know, just like how Shor's algorithm is built for this purpose of factoring, this VQE algorithm is built for the purpose of understanding materials.

1857
02:04:02.233 --> 02:04:06.734
But that algorithm requires you to guess and ansatz.

1858
02:04:07.215 --> 02:04:16.277
And, you know, how Hans Bethe had this idea of guessing an answer and then optimizing around what that answer is.

1859
02:04:22.526 --> 02:04:29.089
at what you think the ground state wave function looks like, and then optimizing around that wave function.

1860
02:04:29.109 --> 02:04:33.251
Well, if your guess is completely out of left field, you're not actually going to get anywhere.

1861
02:04:33.892 --> 02:04:39.274
So it's not like one of these, it's not the dream of Feynman of like, oh, just simulate it.

1862
02:04:39.314 --> 02:04:42.876
You still need a quantum algorithm to do the computation.

1863
02:04:43.236 --> 02:04:50.060
And it's not as simple as like, oh, we just take density functional theory and create a quantum version of density functional theory.

1864
02:04:50.080 --> 02:04:50.220
Right?

1865
02:04:50.940 --> 02:04:53.961
Where like, oh, I know exactly what the electron clouds look like.

1866
02:04:54.001 --> 02:04:57.502
The whole point is that thing is going to tell me what the electron clouds look like.

1867
02:04:57.702 --> 02:05:03.823
So I have to guess first description, and then it only really varies the parameters around my guess.

1868
02:05:04.384 --> 02:05:06.184
If my guess is wrong, I could be in trouble.

1869
02:05:06.604 --> 02:05:12.006
And as I get to larger and larger systems, the probability of my guess becoming wrong gets higher and higher.

1870
02:05:12.266 --> 02:05:17.827
So there's still not a good enough, I think, quantum algorithm to get me the material science algorithm

1871
02:05:19.301 --> 02:05:22.203
promise that Feynman was dreaming of.

1872
02:05:22.923 --> 02:05:31.808
Maybe one person who will help push the envelope there is someone we just covered in our last episode, Omar Yagi.

1873
02:05:31.848 --> 02:05:32.228
Yes.

1874
02:05:32.428 --> 02:05:45.555
Who's just moved out to Beijing, former Nobel Prize winner, 2025, and is the pioneer of reticular chemistry and is pushing this idea of what's being dubbed...

1875
02:05:46.255 --> 02:05:54.021
AI-ometry, which is AI, material science, and chemistry, and trying to basically blend these disciplines.

1876
02:05:54.841 --> 02:06:01.886
And potentially, I know that the quantum piece and quantum algorithms are not necessarily the basis of the concept.

1877
02:06:02.287 --> 02:06:13.855
But seeing where this implementation of AI and speeding up next-gen material science discovery, and then if you add a fundamental quantum algorithm discovery...

1878
02:06:14.355 --> 02:06:18.517
in that context, I think the acceleration becomes very interesting.

1879
02:06:18.557 --> 02:06:19.117
Yeah, yeah.

1880
02:06:19.337 --> 02:06:24.820
I mean, it could be like, we could live in a future where like, AI systems are making the guess.

1881
02:06:25.200 --> 02:06:25.400
Right.

1882
02:06:25.520 --> 02:06:25.721
Right?

1883
02:06:25.801 --> 02:06:29.963
And then they get an answer from the quantum machine, and then they iterate on the guess.

1884
02:06:30.083 --> 02:06:30.843
I mean, who knows, right?

1885
02:06:30.863 --> 02:06:31.083
Who knows?

1886
02:06:31.103 --> 02:06:38.807
Maybe in the future, only AI uses quantum machines because they're the ones creating such amazing algorithms.

1887
02:06:38.847 --> 02:06:39.187
Who knows?

1888
02:06:40.088 --> 02:06:43.311
It's a ripe field, but that's how we got here.

1889
02:06:43.391 --> 02:06:43.611
Yeah.

1890
02:06:44.011 --> 02:06:44.191
Okay.

1891
02:06:44.432 --> 02:06:47.815
And I think that this is a great foundation.

1892
02:06:48.956 --> 02:07:01.467
Again, the whole point of this show is we have an expert and a layman, myself being the layman, a resident PhD, Krishna Chowdhury being the expert, trying to navigate these complex topics and

1893
02:07:01.867 --> 02:07:18.599
at both levels at an expert level so for those who are super technical shout out members of the hrl team that made it through two hours of this podcast uh and literally no one if you did drop it in the group chat i want to i want to hear you guys

1894
02:07:19.439 --> 02:07:28.946
And then the regular everyday people like me that do have an interest and curiosity about some of these things but may not have the foundational tools to be able to dive in and get it.

1895
02:07:29.306 --> 02:07:35.991
And I think that blend is why so many people love the pod because we're able to communicate to two different audiences.

1896
02:07:36.391 --> 02:07:40.734
And so for those who keep asking in the comments, why does Lester just sit there staring the whole time?

1897
02:07:40.754 --> 02:07:41.595
Yeah, first of all –

1898
02:07:42.455 --> 02:07:48.156
Actually, no, this is a family-friendly show, so I'm not going to say what I think I want to say.

1899
02:07:49.097 --> 02:07:54.778
I just, the structure of this show is very much present in other forms of media.

1900
02:07:55.398 --> 02:08:04.340
You have subject matter expert, you have an everyday person, and you're trying to communicate for two different audiences listening.

1901
02:08:05.100 --> 02:08:12.042
And so my job is to smile, listen, and look pretty and sound occasionally kind of smart.

1902
02:08:12.562 --> 02:08:36.448
occasionally be like oh that's good that's what i fight for on this show christina being surprised that i made the oh made that connection that's pretty good um so again part two we're going to actually dive into and hopefully have a physical copy of yes that we can hang on the wall and start our gallery wall in the back of this cover story um quantum silicon processor yeah that's that is correct

1903
02:08:36.768 --> 02:08:38.309
Yeah, you're goddamn right.

1904
02:08:38.469 --> 02:08:48.996
It's going to be so exciting because we will now have this foundation of understanding the history of why this research discipline even began.

1905
02:08:49.716 --> 02:08:55.500
And in modern times, what was arguably the enabling layer to work.

1906
02:08:56.400 --> 02:09:02.585
Having the likes of IBM, Google, Microsoft, HRL, a variety of other players.

1907
02:09:02.725 --> 02:09:04.827
I wouldn't put Microsoft in there, but okay.

1908
02:09:04.847 --> 02:09:07.049
We'll talk about that in part two.

1909
02:09:07.109 --> 02:09:09.371
We'll talk about that in part two.

1910
02:09:09.771 --> 02:09:11.853
But this is now going to get into the fun stuff.

1911
02:09:12.634 --> 02:09:14.595
We, again, appreciate you all greatly.

1912
02:09:14.635 --> 02:09:21.681
If you've made it to the end of the pod and you have not yet given us a five-star on Apple Podcasts,

1913
02:09:22.000 --> 02:09:22.741
or Spotify.

1914
02:09:23.122 --> 02:09:24.905
Now is a great time to do so.

1915
02:09:25.205 --> 02:09:31.376
You're on a jog, you're at the gym, you're sitting in the car in traffic on the way to work or from work,

1916
02:09:32.152 --> 02:09:34.093
It really helps us reach more people.

1917
02:09:34.133 --> 02:09:38.094
We are trying to build the best science show on the planet.

1918
02:09:38.414 --> 02:09:40.854
Share it in the group chat, DMs, all the other things.

1919
02:09:41.675 --> 02:09:45.496
Let's have a – because I always like seeing those who reach the end.

1920
02:09:46.256 --> 02:09:53.038
If you have a comment to leave, you just gave one for – you gave an action for HRL, but that's in the group chat.

1921
02:09:53.218 --> 02:10:01.120
But for the public, if there's one comment to leave because they've made it this far into the pod so that we know who the real fans are.

1922
02:10:03.003 --> 02:10:03.464
What do you think?

1923
02:10:03.944 --> 02:10:05.025
It's tough.

1924
02:10:05.405 --> 02:10:06.145
What would you want?

1925
02:10:06.205 --> 02:10:06.946
What would you want?

1926
02:10:07.086 --> 02:10:10.208
If you had a personal quantum computer, what would you want to do with it?

1927
02:10:10.788 --> 02:10:11.369
That's a good one.

1928
02:10:12.149 --> 02:10:14.030
That's a very good one.

1929
02:10:15.931 --> 02:10:18.353
I have thoughts, but we will save it for the comments.

1930
02:10:18.993 --> 02:10:29.320
My name is Lester Nare, joined as always by my co-host, our resident PhD, and nature cover story co-author,

1931
02:10:30.813 --> 02:10:36.195
Krishna Chowdhury, we are so grateful for you all listening to us rant every day.

1932
02:10:36.495 --> 02:10:37.996
We also have seen your feedback.

1933
02:10:38.596 --> 02:10:44.639
And so we know some of the things you all would like us to do differently as we move forward.

1934
02:10:45.639 --> 02:10:48.841
As we have the opportunity to do so, we will do so.

1935
02:10:48.901 --> 02:10:54.243
We will see you all next week for part two on Quantum Computing.