[afthonos]

"Quantum Supremacy" is a technical term, not a colloquial one. It refers to showing that there exists a problem that a real, physical quantum computer can solve quickly that a classical computer cannot.

Reading the IBM article, they are fully aware of what "quantum supremacy" means in a technical sense, and they are urging the media not to use that term, since it will be misunderstood by the public. Their claim that Google has failed to achieve supremacy rests solely on their claim that they can simulate the circuit far faster (and scale the simulation linearly) using better classical algorithms.

That's a strong claim, and I'm interested in seeing what Google responds with.

Disclosure: I work at Google, but hahaha, no, I'm not cool enough to work on this.

[tagrun]

Physicists here. Note that they say it scales linearly in circuit depth (which is a trivial fact, and has always been true for classical simulations of quantum computers which are optimal in that regard --in fact, that is the case when doing it in the most naive way), not the number of qubits which is the quantum speed up referred in "quantum supremacy".

Another thing, this is actually Martinis' decades long work. I know Google recently started raining money down on his lab a couple years back, helping with the classical aspects, design etc, and media loves reporting as Google's Quantum Computer, but the actual quantum computer, the nitty gritty physics isn't Google's work. Martinis already had a working setup with ~10 qubits when Google started supporting him ~5 years ago.

This IBM "rebuttal" sounds a bit like cheating on multiple aspects, and the timing of the announcement is interesting. Note that they don't tell you how the memory requirements grow with the number of qubits either (which is exponential as well). I expect the response will be new toy computation proposals which will also be prohibitively expensive in classical memory (not just classical CPU with limited memory) in current supercomputers as well. If the experimentalists can roll out more qubits faster though (less likely), the "concern" will be addressed as well.

[afthonos]

Thanks for the detailed response; I am not a physicist, so I didn’t catch the sleight of hand in the linear scaling claim. The timing of the “rebuttal” is almost certainly intentional, and possible because of the accidental pre-publication last month. I hope the rebuttal is indeed specious, because it’s an exciting advance; I’m sure time will tell.

[tagrun]

It's pretty easy and requires no physics, actually.

Here's a simple, extended version.

A quantum gate is, mathematically speaking, a matrix. For a given physical system, of fixed number of qubits, obtaining that matrix on a classical computer takes (on average) a fixed amount of time, let's say T seconds. A quantum "circuit" is a sequence of quantum gates, applied consecutively in time, and you simply multiply them all to get their overall effect.

So if your circuit is made of 10 gates, the total CPU time is 10T, plus the time for 10-1 matrix multiplications. If it is 20 gates, then it is 20T plus time for 20-1 matrix multiplications.

Since multiplying two matrices of the same dimension also takes a fixed amount, on average, the simulation time grows linearly with circuit depth.

The quantum supremacy is related to how T grows as you increase the number of qubits, n (which is exponential, it's a 2^n by 2^n matrix).

[sanxiyn]

No, if you read Google paper, quantum supremacy is entirely about circuit depth scaling.

[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.

[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.

[sanxiyn]

Thank you. I am not sure why people are talking about 2.5 days, since the key claim is "linearly scaling". If simulation is linearly scaling in this regime, the entire proof is indeed questionable.

[mazesc]

IBMs response seems strong regarding "linear scaling", but could they give a complexity-theoretic argument rather than an empirical one?

[sanxiyn]

I think IBM didn't elaborate because it is kind of obvious if you are into this, and if you are not, linearly scaling graph from 10 to 30 is more than good enough. But since we have niche audience here, let's elaborate.

Quantum supremacy is O(n) claim. Then what is n? The answer is that there are two parameters, not one. In Google paper, n is number of qubits and m is circuit depth. n is well known to be difficult to increase. m is not easy either, because if your qubit isn't stable enough, you can't run deep circuit. What Google did is to run n=53 and m=20.

Then, why do you need n=53 and m=20? After all, you could see whether it's exponential by, say, trying n and m from 10 to 15, it doesn't need to take days and years. The answer is that there is time-space tradeoff available and if your n is constant, exp(n) space (but still constant space, since n is constant) poly(m) time algorithm is available, and if your m is constant, exp(m) space (but still constant space, since m is constant) poly(n) time algorithm is available. So if you want to show exponential speedup, you need to be able to exclude these algorithms by increasing n or m enough such that exp(n) or exp(m) space is not realizable. Google chose n=53 such that exp(n) is not realizable, and ran scaling experiment on m.

This is what they mean whey they say in the paper "Up to 43 qubits, we use a Schrödinger algorithm, which simulates the evolution of the full quantum state... Above this size, there is not enough random access memory (RAM) to store the quantum state". Now what IBM is saying is becoming clear. There is not enough RAM, but there is enough disk, so exp(n) where n=53 is realizable, and simulation runs linear in m. It's not a new algorithm, it's exactly the same algorithm Google ran up to n=43. So 43 qubits clearly can't demonstrate quantum supremacy. For the same reason, 53 qubits can't either.

[mannykannot]

Thanks for this clear explanation of the issue! This looks to me like a convincing rebuttal of the specific claim Google made about classical runtime at this particular size, but does it rule out Google claiming supremacy by using the problem constrained such that n == m? Or would Google's device have exponential runtime growth in that variant?

[htfu]

Thanks for the breakdown! But so in other words, it’s still not all that far off that (realistic amounts of) disk storage can’t contain the state and scaling reverts to how they assert it.

[sanxiyn]

Indeed. It's just that 2^53 bytes (about 10 petabytes) of storage is in fact available, so you need a few more qubits to exclude that.

[AlanYx]

It's not quite that efficient... IBM's arxiv paper says "64 PiB of disk space are required for 53-qubit circuits, and 128 PiB for 54-qubit circuits".

Summit has 250 PiB of total storage currently, so it would seem that a 55-qubit simulation is almost within reach by IBM's method as well.

[mazesc]

Thanks a lot, that was insightful!

[skywhopper]

But from the Google blog it sounds like the “problem” they chose boils down to “emulating a quantum computer”. Which doesn’t sound like it’s exactly in the spirit of the test, since the quantum computer can obviously emulate itself—and with zero wasted operations!

[afthonos]

It's exactly the spirit of the test; the missing element is that the circuit they're emulating can scale in qubits. So the question is, if you add one cubit, what happens? Can classical computers keep up? The tests were run on a range of cubits with 50+ being the largest number, which is where the 10,000 year claim comes from. Anything further than that just isn't feasible to compute on classical computers, because they don't scale like that.

So why is this in the spirit of the test? Because this means that there are some problems that can only be efficiently solved by quantum computers. So this establishes "supremacy" in the sense that while a quantum computer can efficiently solve any classical computing problem, a classical computer cannot solve any quantum computing problem.

The distance between having this proof-of-concept and having meaningful speedups on real problems that cannot be matched by classical computers is very large; all this tells you is that it's possible, and looking more might not be a waste.

[marktangotango]

> Disclosure: I work at Google, but hahaha, no, I'm not cool enough to work on this.

I often wonder why people feel compelled to write this. There nothing in your profile or in your post history to prove unequivocally you do or don’t work anywhere in particular so why even mention it?

Edit; responders are citing ethics and company policy; but does anyone really think vague hand wavey speculation on a public message board is relavant to anthing?

Sure if you work in the ads group and you posted "wow, our division is in trouble, competitor Z is really killing it, and our quarter earnings are going to miss big time!" Yeah that matters, but GP? Really?

[otterley]

First, it’s a professional ethics requirement. If there is the possibility of a conflict of interest in our statement, we need to disclose it to avoid misleading anyone.

In addition, there are plenty of ways to figure out where an HN member is employed besides looking at their post history. It’s not necessarily found in publicly available data, but it can be found.

Also, you have to account for future acts. Disclosing early can help insure against accusations about misconduct if you were to out yourself — or someone were to out you — later.

[afthonos]

Company policy. This prevents headlines like "Google had employees secretly astroturf to give traction to their quantum supremacy claims" if someone decides to truly dig. I theoretically could pretend I don't work here, but I find life is easier if I just follow reasonable rules.

(I did forget to mention I didn't speak for Google, but it should be pretty obvious from context)

[AYBABTME]

To disclose possible bias, in this case maybe parent feels like their opinion might be biased toward Google's claim.

[smadurange]

I agree. Possibly to just give a bit more weight to what they say. So far, I've mostly seen this with Google employees here. Can't remember seeing anyone else mentioning this except when promoting a product.

1. Regarding policy, I think a simple disclosure like this is my personal opinion not that of my employer would be good enough. 2. Indicate possible bias: nope, one should always understand any opinion is biased due to many different reasons. So, unless this is a rigorous analysis of something, this is quite uncalled for.