[daveFNbuck]

It's basically that BPP captures all realistic polynomial-time computations. The speedup would have to be sufficient to show something like a problem in BQP that isn't in BPP. I don't think anyone has been able to show that unconditionally yet.

You'd also need to accept that Quantum computers are realistic, which is why Aaronson's trilemma includes quantum computers being impossible.

[wbl]

That's true but Grover search shows that quantum computers can give big speedups so I don't know why I would believe BPP=BQP.

[nabla9]

Grover's algorithm still takes exponentially many operations to solve a search problem that can be brute-forced in exponentially many steps. Much faster, but still in EXPTIME. No jump from exponential to polynomial complexity class.

[scottlocklin]

This sort of statement is exactly why serious people shouldn't take "quantum complexity theory" seriously. The complexity class BQP is bullshit: there are no quantum computers, the end.

Feel free to prove me wrong by building one which does useful calculations. No time limit, until you die, in which case "time's up."

Edit add for downvoters: the strong Church Turing thesis is also almost certainly, and very obviously bullshit. How does that make you feel?

[inflatableDodo]

I'm betting on n. Where n stands for us not fully understanding how causality works yet, or a lot about what the hell is going on in general. I'm also rooting for something interesting emerging unexpectedly from Umbral Moonshine, because who can't help but love the Monster Group? https://www.quantamagazine.org/mathematicians-chase-moonshin...

[thechao]

You’re merely goalposting Scott “Quantum Computing Fists of Fury” Aaronson’s trilemma. If you have proof that quantum computers are physically unrealizable, I’ll happily help you publish that paper. There’s no way my brother could belittle my lack of education if I had a Turing Award or Nobel Prize, or two.

[daveFNbuck]

Which statement are you saying demonstrates why people shouldn't take quantum complexity theory seriously?

[scottlocklin]

BQP doesn't exist: there are no quantum computers. Saying BQP is like saying "magic fairy dust perfect unitary transformers that effectively encode a perfect complex number in the same sense a protractor theoretically can solve NP-complete problems by encoding real numbers."

[doubleunplussed]

The qbits and unitaries don't have to be perfect - it's about how things scale when you add qbits. Quantum error correction shows that you can add more qbits to make up for imperfection, and still be left with a quantum computer, i. e. the imperfection hasn't demoted the thing to a classical computer.

Of course they haven't built one yet, but none of the difficulties encountered so far have involved discovering new physics, which is what you would need to do to rule out quantum computers since the laws of physics as currently understood permit them.

[scottlocklin]

You've just regurgitated Aaronson's statement on the topic. Aaronson never studied physics, and has probably never fiddled with an op-amp or tried to make entangled anything in the world of matter. There's zero evidence quantum error correction will work; it's just an idea with no basis in the world of matter. There's zero evidence you can meaningfully and usefully manipulate quantum coherent states, let alone manipulate an exponentially huge number of them with a polynomially large number of computational elements, which is the essential claim of quantum computing. They make great claims: great claims need evidence; not theoretical wankery. Building a couple of scalable error corrected qubits would be a great start; it might even cause me to shut up about it.

Never in the history of the human race has something as complex as a computer architecture existed in the theoretical world before it exists in some form in the physical world, let alone one for which we define complexity classes.

The entire field is intensely silly, and the last time I said so in a public place, the waiter turned out to be some dude who just got his Ph.D. in the subject. He didn't agree with me exactly, but the fact the dude had a job bringing people steaks for a living is a decent argument I'm right.

[doubleunplussed]

My arguments are my own. I am an atomic physicist, and I meaningfully and usefully manipulate coherent quantum states every day. Not for making a quantum computer mind you, but quantum states nonetheless. Quantum mechanics works. The atoms do exactly what the Schrödinger equation says they should, however much entanglement is added. We are yet to see it break down. Plenty of my colleagues are working on quantum computers, with atoms, ions, photons, and solid state systems, and from where I stand it doesn't look like nonsense. It looks steady progress, and if there are insurmountable barriers, they have not yet been encountered.

I am not certain that quantum computers are possible, but I am certain that you are wildly overconfident that they are not.

[daveFNbuck]

So we shouldn't take research into things that don't exist yet seriously?

[scottlocklin]

Designing algorithms for a computer architecture that assumes matter behaves in a fairly trivially unphysical way sure seems like a glass bead game to me. Especially considering the hype and baloney around this particular one. There are zero actual quantum computer designs (aka error corrected and capable of factoring large or even small integers into primes) under construction: but everyone runs around like chicken little declaring the sky is falling.

I went to a Gordon conference on this subject in the 1990s; as far as I can tell, there has been zero progress in the topic since then. Sure are a lot of press releases though!

[doubleunplussed]

At what odds would you bet that we won't see a quantum computer outperforming a classical computer on any problems in the next, say, 20 years?

[nabla9]

The problem here is that you just state something that looks like strong personal opinion. You vaguely refer to serious people.