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Comment by phkahler | Hacker News Reader

Since the pilot wave theory is deterministic, wouldn't someone be able to simulate a quantum computer with a classical one in reasonable time and storage?

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It is deterministic, but you still need to keep track of a field that covers your whole configuration space (basically you need all the information contained in a function R^n->C for n degrees of freedom). Keeping track this high-dimensional field is what makes a quantum computer hard to simulate in the first place, not the non-determinism. So no, it doesn't make anything easier to simulate.

This makes a lot of sense if you think of it that way: Pilot wave theory gives exactly the same results as any other decent interpretation of quantum mechanics. So the work necessary to simulate it will also be exactly the same. Simulating quantum mechanics is not hard because we don't understand it. It is hard because it is an inherently hard problem (otherwise, how could quantum computers be faster than classical computers?).

Well we don't really know so far whether BQP is bigger than P.

Okay, that is of course true :)

So replace "it is an inherently hard problem" by "it is most likely an inherently hard problem".

The same complexity is there in both cases.

However, there are techniques that allow one to compute the wave function from the Bohmian trajectories. It is just a mathematical trick that certainly does not make BM philosophically more relevant, but it rather neat. This is explored in quantum chemistry contexts. Spin is an issue that stops it from being generally useful, but depending on the context, it is possible.

https://www.crcpress.com/Quantum-Trajectories/Chattaraj/p/bo...

Supposing "deterministic" means "classical", and so only classical computers are possible: since it's deterministic, the entire timeline leading up to turning on a quantum computer is also part of the computation, a prep phase you're simply not counting. So QCs aren't really faster, they just cheat in a way that's not typically observable.

What's interesting is that this actually explains the source of quantum speed up, something no other interpretation can satisfactorily do at this time.

"the entire timeline leading up to turning on a quantum computer is also part of the computation"

why?

Because the computation is just physics too. It's the particles of your brain that moved your hands that typed the program into the computer that will eventually compute the final result by what appears to be a quantum phenomenon localised in space-time, but that really stretches back infinitely.

"just physics", "stretches back infinitely" I feel like You could say this about, well, anything. Afaik, you could take any event and trace its causes all the way back to the Big Bang. But that seems a bit... impractical? Why would we do this with a quantum computer? Am I missing/misunderstanding something?

You're not "doing" anything with a quantum computer. That's just the reality of quantum computation in this conceptual framework.

And no, you can't say that about anything. In particular, you can't say that about non-deterministic interpretations of QM (most of them) because causal chains can only be traced back to the most recent non-deterministic event. In fact, pilot wave theories are among the only deterministic interpretations of QM.

What would make you think that? Deterministic doesn't imply predictable, reducible, or low complexity. Even a purely deterministic simple system can be capable of (and most are) chaotic behavior whose information content would grow faster than any system smaller than itself could predict. In other words, the only way to "simulate" the system would be to completely reproduce every bit of it, and let it evolve in realtime. And practically speaking, we can't even approach that.

For example, the double pendulum: https://en.wikipedia.org/wiki/Double_pendulum.

That said, the phase space of a double pendulum is bounded.

It's really funny that something as simple is impossible to predict over longer times, because you would need perfect information. Yet climate science is 'settled'.

Take an undamped double pendulum and divide the space up into 2 sections. Suppose you can only check which section the pendulum is every N seconds. Every time you check, you record the value, and over time you build up a sequence of K numbers: 1,0,1,0,0,1,1,1,1,0,0,1,0,...

Suppose you know the exact initial state (dx/dt, x) of the pendulum.

What bounds on K and T are required such that the sequence of numbers is asymptotically indistinguishable from a purely random sequence?

So, because of a silly thought experiment, one might think there is very simple order to the apparent randomness. But, as Pauli would say, "it's not even wrong"...

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