I find it very "triggering" when people use this metaphor of uncertainty as a programming shortcut, when my life (currently working on simulating quantum systems) would be substantially (exponentially) easier if reality was classical.

I consider it a universal warning sign when your physical theory postulates that reality works a certain way underneath, and then conspires to keep you from exploiting this way. Superluminal collapse, for instance, or closed timelike curves; it seems to my intuition that these are clearly flaws in the theory rather than properties of reality. In a sense, the sci-fi concept of the ansible, where quantum collapse effects are exploited for FTL signaling, is more plausible than the view where quantum systems collapse instantly, but cannot be exploited for FTL. If your theory requires FTL in the "backend" to operate, it shouldn't end up with FTL just happening to not be exploitable in the "frontend". So I expect that when we find the true ToE, it's not going to end up with traits where the data structure in principle allows a certain capability, but coincidentally doesn't give us access to it; all limitations of that theory would follow directly from its structure, so that illegal operations cannot even be expressed. So when we find a practical limitation to the exploitation of a physical theory, then this seems to me to require, barring very good theoretical reasons to the contrary, a genuine underlying property of the universe that justifies this limit.

As such, it seems to me, purely from an intuitive view, that of those three claims:

- reality is quantum

- quantum mechanics requires exponential cost to simulate

- quantum mechanics cannot be exploited for exponential computation

One has to be false! If reality requires exponential cost to simulate, we shouldn't expect it to then turn around and hide that capability from us. God famously doesn't play dice with the universe; but I doubt he's playing Poker either. Personally, I suspect quantum mechanics is cheaper than is widely believed.

Idk, am I missing something obvious?

As far as we know for now, [a variant of [0] ] this one is the wrong claim: we do have algorithms (Shor's, Grover's) that are faster on Quantum Computers than any known classical algorithm.

Of course, we do not yet have any proof that a faster classical algorithm can't exist, so the possibility remains open that this claim remains true. BUT, if this claim turns out to be true, then it is extremely likely that either one or both of the other 2 claims will immediately turn out to be wrong.

[0] I would note that the "exponential" part is somewhat of a red herring. If there is any kind of asymptotic speed-up that QCs fundamentally have over classical computers, even if it's just quadratic, then the larger point will remain valid.

> In a sense, the sci-fi concept of the ansible, where quantum collapse effects are exploited for FTL signaling, is more plausible than the view where quantum systems collapse instantly, but cannot be exploited for FTL.

This is also what rubs me the wrong way about entanglement, and seems a very tantalizing thread to pull at if one wanted a more fundamental theory. The other thread of course is the measurement problem.

The Schrodinger equation almost always predicts that a particle has some particular amplitude at many different locations. However, if you try to detect a particle, you will never find it at more than one location. Furthermore, once the particle is detected at one particular location, you need to update the Schrodinger equation to give it amplitude 1 at that location and 0 everywhere else - if you don't perform this nonlinear update and instead use the old wave-function, the predictions for further experiments will be completely off.

Now, the physical interpretation of this collapse varies wildly between different interpretations of QM, but some variant of it is always required - otherwise, the observations simply do not match the math. We don't yet have any theory consistent with QM that can make predictions without applying the Born rule.

[1] https://arxiv.org/abs/0906.2718

The current consensus (at least among people I speak to) is that a quantum computer will probably be able to solve some problems which are in NP (and not in P), but will probably not be able to solve an NP-hard problem.

Your intuitive view is appealing, but I don't think one should get too hung up on intuition. Our intuition was honed for millions of years to avoid large wild animals and avoid falling out of trees in prehistoric Africa. It generally sucks pretty badly at making guesses about the fundamental nature of the universe (or at least mine does).

Edit: by the way a faster than light communication "ansible" is functionally equivalent to a machine that sends messages back in time. I disagree with your view that such a machine is more plausible than the view that some ftl stuff happens on the "backend" but is hidden from the "frontend". Having said that my view is that there is no ftl stuff on the back or front end, this is consistent with something like the many worlds interpretation of quantum mechanics, which is entirely local and causal (no ftl stuff).

Disagreeing again with the "Ansible is unrealistic" view: I agree it's unrealistic in a global sense, I just think all of its unrealism comes from the use of FTL in the backend. FTL + relativity produces timetravel, yes. I just think it's implausible to expect a physical universe to first provision the mechanics for FTL, then provision a system that gives you timetravel when exposed to FTL, and then very carefully separate those two systems so that they computationally never touch, even though in theory they could! and so in a sense, this physical theory implies that this universe has to be prepared, in principle, to allow time travel and account for it, and having gained this capability has elected to specifically not use it. It just stinks of a massive Occam violation - the potential for time travel is an "entity without necessity", and the theory is bloated by it twice over; once by its inclusion in the physical logic and once again by the additional exclusion mechanism that makes it unusable in every reachable state. And so the ansible universe pays slightly less cost just by leaving out the global censor.

Am I saying "no correct theory can look like this"? No! I am saying it enters the race with a huge handicap.

My understanding is that that is a yes - with a quantum computer, quantum simulations [are expected to] run in linear time instead of the current exponential time.

Then you give me two numbers a and b (with some technical constraints) and ask me whether the ground state energy of H is between a and b.

This problem is QMA-complete as long as k >= 2, and known to be QMA-hard even for some pretty nice looking Hamiltonians. Here QMA stands for Quantum Merlin-Arthur which is the complexity class equivalent to MA (Merlin-Arthur) for classical computers. You can think of MA as being related to BPP in the same way that NP is related to P, and this is the same way that QMA is related to BQP.

Basically QMA problems are not expected to be solved efficiently by a quantum computer.

That is, if we think that the universe is a simulation running on a classical computer, then quantum effects such as the uncertainty principle CAN'T be a "shortcut" to make the simulation easier - as in fact they make the simulation literally exponentially harder. If we assume that the universe is a simulation running on a quantum computer, then quantum effects are fundamental anyway.

Of course, everyone understands that this is a simple joke. Still, it's interesting that it goes completely against our intuitions as computer simulation designers.

PBS Spacetkme has a great video on pilot wave.

Getting rid of all the messy probability issues is amazing.