# Tag Info

15

Google's paper/results are kind of sideways to questions in computational complexity about the relation between $\mathrm{BPP}$ and $\mathrm{BQP}$ (and even further from questions about whether $\mathrm{P}\ne\mathrm{NP}$). It's more as if Google relies on the hypothesis that $\mathrm{BPP}\ne\mathrm{BQP}$ as evidence that their quantum computer performs a ...

13

It's just a coincidence. I can speak from personal recollection on the Google side. Google originally intended to use a 72 qubit chip (Bristlecone) where qubits were essentially directly connected to each other. They then switched to an architecture where qubits were connected indirectly via a coupler. The coupler requires a control line, so this increased ...

6

They say in Section X.H of the supplement that the Summit supercomputer has a power capacity of 14 megawatts. They compare that to their own setup. Their power consumption is mainly their dilution fridge, which they say is about 10 kilowatts plus about another 10 for chilled water for its supporting equipment. Their own supporting PCs and other ...

5

What does "obtaining samples" mean in this context? The same thing it means in a more classical context. Consider the probability distribution of the possible outcomes of a (possibly biased) coin flip. Sampling from this probability distributions means to flip the coin once and record the result (head or tail). If you sample many times, you can retrieve ...

5

TL/DR: The two-qubit gates are going by the moniker "Sycamore gates" in the paper, and it appears that they would ideally want to explore more of the $(\phi, \theta)$ phase-space but for their purposes (of quantum supremacy) their current Sycamore gate is sufficient. The pattern of gates $\mathrm{ABCDCDAB}$ was chosen to avoid "wedges" and maximize/optimize ...

4

In relating quantum computing to classical computing there may be a small conceptual hurdle that needs to be overcome. Although a classical $\mathsf{NAND}$ gate may be implemented in hardware (say CMOS with a set of N- and P-type transistors), the idea of a quantum gate such as a $\mathsf{CNOT}$ or an $\mathsf{H}$ gate used in quantum computing most often ...

4

The model's accuracy is purely empirical observation. The error trend (Fig 4, or 41:50 in the video) demonstrates that the error of the system (cross entropy fidelity with respect to simulated results) is tracked closely by the "high school probability" model he mentions. The way this basic model would work is to assume 1- and 2-qubit gate errors are ...

4

That seems to restrict the output probability distributions of all quantum circuits to rather high entropy distributions. The output of a typical randomly chosen quantum circuit is rather high entropy. That doesn't mean you can't construct circuits that have low entropy outputs (you can), it just means that picking random gates is a bad strategy for ...

3

Paraphrasing some tweets on the matter earlier, the result is rather underwhelming because it plays on a discrepancy between what they mean by quantum supremacy (QS) and what people tend to think QS means. What I find most people think QS is supposed to mean, and what I assumed it meant until a month or so ago, was that there exists a computable problem (in ...

3

While a follow-up question asks for the motivation behind the two-qubit gates used in Sycamore, this question focuses on the random nature of the single qubit operations used in Sycamore, that is, the gates $\{\sqrt{X},\sqrt{Y},\sqrt{W}=(X+Y)/\sqrt{2}\}$ applied to each of the $53$ qubits between each of the two-qubit gates. Although I agree with @Marsl ...

3

Although it doesn't explicitly say it in the paper from Google, the diagrams in the paper are missing a qubit along the top edge. Most likely this is the "bad" qubit that wasn't used.

3

When I visited the Google Hardware Lab, they were extremely secretive about everything. It is unlikely anyone will be able to answer this question except for the narrow range of Google Hardware Lab employees, and the ones I know are not very open about what Google is doing. What I can do is answer what a different superconducting-qubit hardware company (D-...

3

In the framing of the question (which I believe to be asked in good faith), there seems to be at least two objections. Sampling from a set of strings is not clearly a function, and Sampling is a physical process, outside of computation. Initially, with regard to the first objection, I assert that sampling is a function, as a search problem. For example, ...

3

The Church-Turing thesis is not in and of itself a rigorous concept, but rather a judgment on rigorous concepts of computability. As such, it's negotiable. The language in Rosser's 1939 expository paper about provability and computability is biased towards deterministic algorithms. There is an important simplifying theorem here: If you only care about ...

2

My guess is that this is an example of co-opetition, i.e. collaborative competition. Number of qubits is just a single characteristic of a quantum processor, but there are a lot more, like tolerance, topology, etc. Also this characteristic is the only one that most people understand. Thus it's not reasonable to put all the resources on the increasing just ...

2

As an initial matter, I think the Supplementary Information (linked in some other answers on this sight) has a significant amount of discussion on $\mathcal{F}_{XEB}$. However, as I understand it (misunderstandings are my own): There is indeed a concentration of outputs from a random quantum circuit, away from a state wherein the square of the coefficients ...

2

This answer only addresses the part about the necessity of the randomness of the circuit because I am by no means familiar with the physical implementation of the qubits at Google and what kind of constraints these impose on the implementation of certain gates. Now, for the randomness: Consider the problem of sampling from the output distribution of a ...

2

Generally speaking, to prove quantum supremacy, you don't need to sample several times from the same unitary/circuit/output probability distribution. If you extract even a single sample from the output probability distribution of a circuit which you know is extremely hard to simulate classically, then you already achieved something that you couldn't do (...

2

In the Sycamore paper linked in the comments, in the description of FIG. 4, the authors state: ...For each $n$, each instance is sampled with $N_s$ between 0.5 M and 2.5 M... For $m=20$, obtaining 1M samples on the quantum processor takes 200 seconds, while an equal fidelity classical sampling would take 10,000 years on 1M cores, and verifying the fidelity ...

2

In fact, you would need an astronomical circuit depth in order to get close to a uniformly random state, or even close to a randomly chosen probability distribution on the $2^{53}$ outputs. As a first estimate, consider how many different distributions you need in order to be within 1/8 of the total variation distance of any distribution on $N$ outputs. ...

2

After some further consideration I think it's quite clear that the only probability mass function evaluated in the computation of $\mathcal{F}_{\text{XEB}}$ is that of the classically computed ideal distribution, denoted $P(x_i)$ in the main paper. This leads me to the conclusion that the phrasing of the following excerpt from section IV.C of the ...

1

Both IBM and Google unveiled 53-qubit processors. At this time, only Google published performance metrics such as 1- and 2-qubit gate errors. Until IBM publishes similar metrics we simply cannot even tell whether Google's processor outperforms IBM's. What we can tell is that the connectivity of the two processors is different - Google's Sycamore processor ...

1

I'm sure that this has something to do with quantum decoherence or "noise" which is caused when more qubits are added. It's likely that they are both at the frontlines of research so 53 qubits are the best that they can do given the hardware that they have access to. As they add more qubits it gets tougher to compute and prompts them to find some suitable ...

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