Why simulate physics with a quantum computer?
Feynman's key insight was to invert the usual view of quantum mechanics: instead of treating it as a source of noise to be managed in classical chips, he asked what would happen if you built a computer that runs on quantum mechanics to simulate quantum systems. The core problem motivating this is that quantum probability distributions cannot be factored into independent parts, a consequence of Bell's theorem. For an N-particle quantum system, a classical computer cannot assign each particle its own subroutine and scale linearly. It must instead track the fully entangled joint configuration of all particles, which is what makes classical simulation blow up in cost.
- The hosts use a two-state spin particle, one that can be spin-up or spin-down, as the concrete example of where this joint-probability storage problem first appears.
- Krishna contrasts the quantum case with what linear scaling would look like: a classical program with n independent data tables or subroutines, one per particle, where memory and processing time grow proportionally to n.
- The Lego block analogy is used to make entanglement concrete: you cannot treat two entangled particles as two smaller blocks that combine into a bigger one, because there is no valid description of each particle in isolation.
Transcript
This chapter, from the episode video's captions · 586 words
40:20everyone thought of quantum mechanics as a nuisance. Because when you're trying to make semiconductors into chips, quantum mechanics is a nuisance. Stuff is moving around, right? There's like you got to worry about the band structure, but if you're if your growth is not great, then the electrons are going to hop everywhere. There's all sorts of noise. And quantum mechanics is primarily that source of noise, right? You got quantum t tunneling, the thermal fluctuations. It limits how small you can make your transistors, things like that. Fineman inverted this perspective >> and he analyzed what if you could create computational complexity by simulating quantum mechanics using a quantum computer a computer that uses
41:01quantum mechanics. Now why would we want to do that? Well, literally reality is an interacting quantum system of particles, right? Like quantum mechanics is the reality. And um 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. So it certainly makes sense. So here's what Fineman said. He said, "Suppose I want to simulate the physics of these interacting particles, right? How much stuff would I need to store in my classical computer? >> Mhm. >> This is where Bell's theorem came in. >> Okay. >> Mhm. >> Remember I was harping on earlier this
41:42idea that the physics of two particles cannot be factored into two independent mathematical probabilities. >> We have to look at it as one Lego block, not two smaller Lego blocks that make up this bigger Lego block. >> Yeah. Yeah. 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? instead there there's no way to combine them later on, right? Um if you could then simulating an n particle quantum system with a classical computer would be pretty straightforward. You just create some kind of software program that assigns like n independent data tables or sub routines for all of the n independent particles. You look them up. Each is tracking some kind of isolated
42:22local state. And then your memory and processing time scales linearly like the order of n like however many particles you have that's about you know how it's going to scale. >> The point being it's just becomes a compute and power. >> Yeah. Yeah. And you make a bigger computer right you could infinite you could scale up to some upper bound that then covers all the types of >> Yeah. >> simulations you're trying to >> and you just have like one subruine for each particle and you're fine and you're fine. Right. But quantum probability distributions do not factor. >> That's what Belle showed. Right. Right. If you want to talk about reality, the experiments show this, right? This is no longer in our head.
43:04>> Right? For an N particle system, you can't decompose it into n different things. Instead, you have to worry about all of them combined. it depends globally on the fully entangled configuration of of your particles, right? So, even if you imagine like a two-state particle like the one that we talked about with Alice and Bob, right? You've got a two-state particle of spins um that can be like, you know, spin up or spin down. Um, a classical computer would be forced to store and update a joint probability
From How Quantum Computing Actually Works (Part 1)
Part I of our quantum computing deep dive traces the field from Bell and Feynman to Deutsch and Shor—and explains what quantum computers actually do differently from classical machines.