The double-slit experiment as a computer
The double-slit experiment shows that light, and even single particles like electrons or photons, produces an interference pattern when allowed through two openings simultaneously. When only one slit is open, you get a single gaussian lump of detections; when both are open, constructive and destructive interference create bright and dark bands. Feynman's path-integral formulation explains this by saying a particle travels all possible paths at once, and probabilities are calculated by summing over those paths rather than using a wave function.
- The hosts are building toward the double-slit experiment as a physical analogy for the Deutsch-Jozsa problem, making the interference pattern directly relevant to quantum computation.
- Feynman's sum-over-paths approach, unlike the wave function picture, extends naturally to quantum field theory and is the foundation of Feynman diagrams.
Transcript
This chapter, from the episode video's captions · 615 words
1:26:15and I want to try to create a version of the double slit experiment that computes my Deutsch Joa >> problem. Okay. Now, to introduce the double slit experiment, um you've got a laser with coherent light. That light falls on two slits 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 a lump of P1 or P2, that's
1:26:57the the first sort of two gausian that I see. But if I don't cover either one, and I I I let the light go through both, >> then I get this interference pattern, right? 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. 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. And I'm going to get destructive interference >> which is at the boundary of the dark pink and the light pink. Yeah. In this in this visual here. >> Yeah. Yeah. Yeah. Yeah. Okay. So, so this is how the double slit experiment works for like light waves and things
1:27:37like that. Now, crucially, it's been shown that single particles also do this, right? I can 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 um single photon >> interference >> like interference on my detector. Right? So Fineman took a look at this and he had a different way of explaining it. Fineman had this idea that of um the path formulation sum over all paths of quantum mechanics and he explained all of quantum mechanics using the sum over paths. He didn't like the wave function
1:28:18analogy. He he came up with his own and it turns out that it's it's really good because it like has applications to quantum field theory and if you know about fineman diagrams that's that's all this sum over path stuff. Okay. So here's how he explained it. This is this is directly from um one of his um Fineman lectures of physics. I've added the red lines and things like things like that. Okay. So um on the left I've got an electron gun. Again, I've got those two holes and I've got a detector on that side. Here's what he says. 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
1:28:58there. >> Okay. What I want the only thing I can do is calculate the probability that the detector is going to register an electron there. Okay. And what I want to do is calculate what is that probability. What's the probability that I'm going to see an electron here or here or here or anywhere else. Okay. He said the electron is going to go through all of the paths. And the way we're going to keep track of what the electron is doing is I'm going to assign um I'm
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.