[tagrun]

No idea where exactly you got that idea (feel free to quote any part of the paper), but no, it isn't.

Even the brute force "simulation" of a quantum computer is like UN...U2.U1 where Us are unitarity matrices. The hard part is obtaining those unitaries (whose dimensions grow exponentially with the number of qubits). For fixed number of qubits though, once you have N unitaries, you do N matrix multiplications. If you double N, it'll take twice long on a classical and roughly twice on a quantum computer (different gates take different amount of time to implement). But on an actual quantum computer, there are tricks you can do (if the Hamiltonian allows) which may allow you to do it in fewer unitaries.

Circuit depth is still important because it is important 1) for modelling the noise in the device and extracting gate fidelities, that's basically how randomized benchmarking works although they're doing something else for fidelity estimates it still is a function of circuit depth 2) for doing anything meaningful when using a given set of basic building block gates.

[littlestymaar]

From the blog post (I haven't read the paper yet) that's also what I understand

> we ran random hard circuits with 53 qubits and increasing depth, until reaching the point where classical simulation became infeasible

Or am I misunderstanding something? (ELI5 plz, I'm not well-versed in quantum computing).

[tagrun]

They're using a "clever trick" to approximately evaluate the overall gate from this paper https://arxiv.org/abs/1807.10749 which is computationally cheaper than doing a "brute force" simulation (which scales linearly in the number of gates), but it quickly becomes worse as you increase the number of gates. That's basically what it says.

It looks like Martinis' group thought a "brute-force" simulation for 54 qubits is impossible, and this appoximate and "clever trick" is the only way to go at this number of qubits, but IBM says that with some different tricks, 54 qubits is still doable (I'm just guessing what they were thinking, and this is the only plausible explanation I can think of).

Overall, a discussion which has nothing to do with quantum supremacy really...

Whether it is a factor of a million or thousand though, the gap between a quantum computer will increase exponentially as the number of qubits is increased. This is fact, assuming quantum mechanics is correct.

Actually, physicists have been trying to deal with this painful fact for quite a long time: it is also the reason why many body physics is so hard computationally and we spent almost a century to develop approximate methods to calculate even the simplest idealistic situations even with hundreds or thousands of atoms using density functional theory, quantum monte carlo etc etc. The whole idea of quantum computation is to turn this difficulty upside down and try to use it into our advantage.

[sanxiyn]

> The gap between a quantum computer will increase exponentially as the number of qubits is increased. This is fact, assuming quantum mechanics is correct.

I agree, but then there is no need to prove quantum supremacy after all. This entire business is about whether quantum mechanics is correct or not.

[tagrun]

Quantum mechanics is about a 100 years old, and no violation has even been observed in laboratory, particle accelerators or outer space. The quantum theory is the most accurate theory we ever had in the history, tested to less than 1 in a billion precision. Even classical computers rely on it. Physicists don't have doubts about the quantum theory, we know it is possible, the problem is an engineering problem of attaining precise control over quantum systems, which is a very very hard engineering problem but there is nothing in physics which says it can't be achieved.

There is still a need, but it is for an entirely different reason: not everyone (people with money and funding agencies, in particular) is physicist.

[sanxiyn]

General relativity is also 100 years old, no violation etc. Still, discovery of gravitational wave was very welcome, because test of general relativity in strong force regime was not very good.

Quantum computing is analogous: test of quantum mechanics in "strong computational regime" is scant. You seem knowledgeable, but your comments on current claim of quantum supremacy is akin to, say, when claim of discovery of gravitational wave was made and then disputed, replying, "gravitational wave will be discovered, this is a fact assuming general relativity is correct, general relativity is 100 years old, no physicists doubt the theory" etc. All true, but rather pointless.

[tagrun]

It's a very different thing. I'm not just talking about the age of the theory. I'm talking about the length of the period during which it was tested so many times, to the level of precision that no other theory got tested and stood.

General relativity was, and still has never been tested to anywhere near that level of precision, and that many times. And in fact, we still have strong reasons to doubt general relativity because there may or may not be deviations from it observed in galaxies and large scale universe.

General relativity may be correct in that scale (with the ad-hoc addition of a cosmological constant) but to be consistent with those observations, one requires the existence of black holes, dark energy and and dark matter, things we never truly observed and don't know for sure exists (although it is our best explanation at this moment).

We don't really understand how gravity behaves in very small scales, extremely large scales, or in the presence of very strong energy densities. One thing we know for sure is, general relativity is not the ultimate theory of gravity, it spectacularly fails in very small scales.

We would like to stress-test all aspects of general relativity to 1 in a billion precision as well, but we can't.

This is basically because gravity is very weak and you can't design all sorts of controlled experiments to test it. The best you can do is to make observations in the vicinity of readily massive things like Earth, Sun or a black hole, which you have no control over. You can't make two black holes, pit them together and see what happens in the lab. A situation very different from the quantum theory.

Physicists did expect to observe gravitational waves, and it wasn't a shocker to anyone. The thing that makes is very big deal for physicists is that we now have a whole new way probing things that we couldn't before, in particular things which we don't understand yet, including the violations of general relativity which we do expect to see.

We don't expect to see deviations in quantum theory (unless you bring a black hole nearby your quantum computer).

[YeGoblynQueenne]

The theory of epicycles very accurately explained observed phenomena, and though the conditions for science at that time were very different, its popularity and accuracy very much comparable to those of quantum theory.

In the Hipparchian and Ptolemaic systems of astronomy, the epicycle (from Ancient Greek: ἐπίκυκλος, literally upon the circle, meaning circle moving on another circle[1]) was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. In particular it explained the apparent retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth.

(...)

Epicycles worked very well and were highly accurate, because, as Fourier analysis later showed, any smooth curve can be approximated to arbitrary accuracy with a sufficient number of epicycles. However, they fell out of favour with the discovery that planetary motions were largely elliptical from a heliocentric frame of reference, which led to the discovery that gravity obeying a simple inverse square law could better explain all planetary motions.

https://en.wikipedia.org/wiki/Deferent_and_epicycle

So the epicycles worked very well to explain and predict observations, but for reasons irrelevant to what really caused the motion of the planets. It's still possible that quantum mechanics will fall in the same way.

Note I don't have a horse in this race. I have no opinion on whether quantum mechanics is right or wrong.

[trhway]

>Quantum mechanics is about a 100 years old, and no violation has even been observed in laboratory, particle accelerators or outer space. The quantum theory is the most accurate theory we ever had in the history, tested to less than 1 in a billion precision.

sorry, i think you're doing a slew of hands here. Quantum computing relies not just on QM, it relies on Copenhagen interpretation of it - superposition being a physical reality, not just statistical description. That interpretation is tested by the Bell experiments and granted where have been a bunch of them which do look like confirming the Copenhagen.

>Even classical computers rely on it.

all that confirms QM, not the Copenhagen interpretation. Wrt. Google supremacy demonstration - it would work the same in statistical aggregate interpretation too thus actually not showing anything quantum computing.

[tagrun]

No. An interpretation is just that. No matter what interpretation you use, the experimental measurement results are the same.

If they don't give the same results, it won't be interpretations: you'd have two competing theories and one of them will be wrong since it can be ruled out experimentally.

This is also why majority of physicists don't care much about such philosophical aspects. You can argue that they should, are there are a few people working on foundations of quantum mechanics, but most physicists (including me) see it as semantics and choose to spend their time on practical physics. At least that's what my field (condensed matter physics) is about, which also encompasses the realization of these quantum computers. You can't change the conductivity of a material, or the measured charge state of a transmon qubit by using a different interpretation.

[mlyle]

I don't think most critics are doubting quantum mechanics. The question is whether quantum computers can reasonably (as an engineering challenge, as a factor of cost, etc) be scaled and can be adapted to take on important real-world problems better than classical computer systems in practice.

We are getting more and more proof points and eliminating a lot of the doubt but this has not been shown yet.

[tagrun]

Actually, we had people who claimed for about four decades that it is fundamentally impossible to have quantum speed up, basically equating it to a perpetual motion machine. We still have such famous people around (who aren't physicists, of course), now a loud minority, and "quantum supremacy" was coined because of/for them.

What you're describing is mainly the new generation of people who grew up hearing about quantum computers on the news about experimental realization of small-scale (a few qubits) quantum computers.

[mlyle]

Eh, I haven't really heard them. I'm 40 and have followed this from near the beginning (starting with reading Science News in the late 80's-- even then the criticism was pretty muted).

I am not positive we are going to get quantum computers with error correction on boolean qubits that can do all the meaningful tasks we hope quantum computers can do. I think it's more likely than not, but it is not close to happening and may never happen. I am not even 100% certain (but it is very very likely) that it is physically realizable.

In my view, this current milestone is kind of contrived.

And even if we do, it's not clear what subset of tasks currently performed on classical computers will be superseded by quantum computation. That's perhaps one of the biggest problems: normal computing has had a whole lot of use cases to pay the research and capital costs.

[sanxiyn]

Exact quote from the paper: "algorithm becomes exponentially more computationally expensive with increasing circuit depth". See also figure 4b, where circuit depth scaling is graphed.

[tagrun]

That sentence actually reads "Schrödinger–Feynman algorithm becomes exponentially more computationally expensive with increasing circuit depth" which is true (because the paths in a path integral in a discrete setting would grow combinatorically, but don't have to sort to path integrals to approximate the unitary in a "quick" and dirt way, which clearly doesn't scale well --in fact, if you avoid such "clever" tricks [which is only beneficial in some limited regime] and do it in the naive way, it will scale linearly). It's not the only game you can play on a classical computer, as IBM points out (for which the upfront cost is much higher).

Figure 4b is about error estimation, They use XEB which is exponentially faster than, say doing full quantum process tomography, which is also true. That's the whole reasoning behind XEB, which gives far less information about the error channels, but you still have a fair estimate on the overall fidelity.

None of these have anything to do with the complexity of the actual computation done on the quantum computer though.

[sanxiyn]

Indeed these don't have anything to do with quantum computers, but it does have something to do with quantum supremacy, because quantum supremacy is a claim about both quantum computers and classical computers.

Google chose an algorithm exponential in circuit depth as the best classical algorithm in order to establish quantum supremacy. IBM demonstrated (as you agree) it is in fact not the best classical algorithm. IBM is entirely correct to point this out.

[tagrun]

Again, no.

It is a trivial fact that on a classical computer, you can simulate a quantum computer in time that grows linearly in circuit depth, in principle (as in the case of the "naive" way I mentioned above). No one in doing quantum algrothims ever claimed this was the case, and claiming otherwise is just a silly mistake.

Preskill coined the word "quantum supremacy", not Martinis. Even if someone from Martinis' lab misspoke, you can't pin it on Preskill.

Take Shor's algorithm, which has been the poster boy of quantum computing for decades. It gives exponential speed up in the number of qubits, not circuit depth.

See other examples here: https://quantumalgorithmzoo.org/ The complexity is in the number of qubits, "cirucit depth" is a non-concept in quantum algorithms.

No one cares about the circuit depth in quantum algorithms, because in principle, you can always reduce the circuit depth to 1 on a quantum computer: quantum computers aren't necessarily made of basic logic gates, you can implement any unitary in by for example smoothly pulsing the fields in a correct way in a single go.

"Depth" is a concept which usually comes into play when you try to measure the quality of the implementation of some given gate U. You repeat U many many times say M, and see how some measured quantity decays as a function of M, which gives a measure of the fidelity. But this has nothing to do with the quantum algorithm's complexity, it's just for "benchmarking" a physical implementation of the gate.