
The Question of Quantum Supremacy - lainon
https://research.googleblog.com/2018/05/the-question-of-quantum-supremacy.html
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nl
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)

~~~
teawithcarl
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.

~~~
justifier
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'

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ivan_ah
The arXiv links: \-
[https://arxiv.org/abs/1608.00263](https://arxiv.org/abs/1608.00263) \-
[https://arxiv.org/abs/1709.06678](https://arxiv.org/abs/1709.06678)

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

~~~
baking
[https://arxiv.org/abs/1605.03590](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."

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mchahn
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.

~~~
Sniffnoy
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.

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

~~~
sgt101
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?

