I'm Scott Aaronson, quantum computing/computational complexity researcher. AMA

Hi Scott,

David Deutsch, in his book "The Fabric of Reality", gives example of a problem that is presumably easily solvable by the quantum computer. On the other hand, he explains that the total number of particles in the universe is smaller than number of computations that will take place. The question that he poses is where the problem was actually solved? His answer is that there parallel universes, and the computation is performed in these universes. He also stipulates that the "weird" quantum behavior of particles, such as spooky action at a distance, all could be explained by the multiverse. What is your opinion about the multiverse and potential of quantum computers to solve quantum physics problems?

It's not obvious why you'd want to talk about complex amplitudes, whose squared absolute values are probabilities, outside the context of quantum mechanics. Maybe a better way to say it is: once you're talking about such amplitudes, essentially by definition you ARE talking about quantum mechanics. :-)

Having said that, in classical probability theory, it's sometimes useful to look at the (positive) square roots of probabilities, for example to get a distance measure between probability distributions. See here:

https://en.wikipedia.org/wiki/Bhattacharyya_distance

Also, we've often been able to use quantum tools to prove new results even about classical theoretical computer science. See here for a beautiful survey, though one that's already a decade out of date:

https://arxiv.org/abs/0910.3376

In this way, the mathematical tools that we've developed in quantum information can "pay rent" in classical CS, even if we counterfactually imagined that our world wasn't quantum-mechanical at all. It would take some time to go through an example of this, but (e.g.) it was shown that if a certain classical error-correcting code existed (called a 2-query locally decodable code of subexponential size), then an even better quantum error-correcting code would also exist, but the latter was something that people already knew how to rule out.

In these situations, some people would argue that we're not "really" using quantum physics or amplitudes; we're just taking MATH that was developed for that purpose, and repurposing it for something else. But it would be weird to say in a talk, "I'm now going to introduce a unit vector of complex numbers that's just an ordinary vector, nothing physical at all about it, then apply the following tensor product of 2x2 and 4x4 unitary matrices to it...," when everyone knows full well that all your intuition about this came from quantum states. Indeed, I confess that even when I'm doing linear algebra that has nothing to do with QM---i.e., my vectors really are just vectors of real or complex numbers, not amplitudes---I sometimes slip up and use the physicists' notation for quantum states (called the Dirac ket notation).

Hey Scott, thanks for doing this.

What do you think of the Copenhagen Interpretation especially in light of the delayed choice quantum eraser experiment[0]?

I know interpretation of QM is something actual working scientists try to avoid (I know I do such for my little corner of physics) but given how much interpretation informs intuition it's worth considering once in a while.

[0] https://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

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There's a related comment here[1]. The simpler version of the bound doesn't depend on mass or energy, just surface area (or radius for a Schwarzschild black hole). It seems to me that 2^72 of "storage" is already pushing it, but anyway I don't understand why the number of bits needed to "describe" the state isn't the relevant quantity. IIRC Bekenstein had at least one completely classical derivation of the bound.

[1] https://www.scottaaronson.com/blog/?p=2428#comment-786973

"not to mention our own brains"

Is this a known known that our brain doesn't use QC?