The Question of Quantum Supremacy | Hacker News Reader

The Question of Quantum Supremacy

research.googleblog.com

93 pointslainon11 comments

This is a pretty dense read.

My summary (and I’d appreciate correction from those who follow this more closely):

There is a set of problems where the runtime complexity increase exponentially as the problem size increases on classical computers.

If you can show you have a device where the time complexity only increases linearly and you are faster in clock time then you have shown that your device is superior to classical computing.

Here Google chooses a problem and shows that their 9 qbit quantum device (which they developed) shows exponential speed up between 5 and 9 qbits.

They project that speed up and error rates forward and find it should achieve quantum supremacy at 50 qbits.

(At least that’s my reading. Corrections and expansion very welcome)

Yes, I believe you catch the gist of it.

It’s a calculation which proves there is indeed a complexity point whereby quantum computing will exceed classical computing ... by proving mathematically that adding enough qubits will suffice that.

Keep in mind this proof still hints at “a class of problems/calculations” which qubits will overwhelm, not a general overwhelming of everything. At least that’s my reading.

Still this mathematical proof is indeed interesting.

gp> it’s a calculation which proves there is indeed a complexity point whereby quantum computing will exceed classical computing

'Prove' is correct for the research but a bit strong for the language of your summary

The important caveat:

tfa> determination of the smallest computational task that is prohibitively hard for today’s classical computers.

'today's classical computers'.. or more timeless: 'contingent on p!=np'

The arXiv links: - https://arxiv.org/abs/1608.00263 - https://arxiv.org/abs/1709.06678

Didn't understand the relation between quantum computing and nitrogen fixation.

Me neither, I am feeling perplexed.

https://arxiv.org/abs/1605.03590

Elucidating Reaction Mechanisms on Quantum Computers

"We show how a quantum computer can be employed to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical-computer simulations for such problems, to significantly increase their accuracy and enable hitherto intractable simulations. Detailed resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. This demonstrates that quantum computers will realistically be able to tackle important problems in chemistry that are both scientifically and economically significant."

If I understand the problem correctly it involves generating random strings. If so, then it seems like cheating since quantum effects are random and classical computing isn't.

That's not really what's going on here. Typically when quantum computers are compared against classical computers, it's assumed that the latter have access to a source of randomness. It's not the randomness by itself that should make this hard for a classical computer.

Are they saying that their simulations of quantum computers with classical computing aim to break new ground in terms of computation?

They are saying that they want to demonstrate a convincing point from where it's infeasible to use the tactic of breaking new ground classically to simulate quantum devices breaks because the exponential complexity means that the classical devices are beyond our capability as a society, and will remain that way for at least a long time if not forever. At that point having a quantum computer that is constructible and can do these problems is at least valuable for this task. Until then the only point of quantum computers is that it's an interesting idea. But, quantum supremacy is just a first step; simulating quantum devices of various sorts is important science, but there is a long way to go before quantum computing can be implemented that is useful for the rest of the feasible tasks that people talk about using it for. I would like to see a list of the tasks that are understood to be targets for quantum computing and a projected timeline - has anyone got one? When do people in the community believe that we will have a workable device that can do Grover's algorithm for 10^52 bits?

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