Googles Quantum Supremacy Claim Data Documentation and Discussion Gil Kalai Yosef Rinott and Tomer Shoham

2025-05-06 0 0 464.21KB 32 页 10玖币

侵权投诉

Google’s Quantum Supremacy Claim: Data,

Documentation, and Discussion

Gil Kalai, Yosef Rinott, and Tomer Shoham

January 26, 2023

Abstract

In October 2019, Nature published a paper [3] describing an ex-

periment that took place at Google. The paper claims to demonstrate

quantum (computational) supremacy on a 53-qubit quantum com-

puter. Since September 2019 we have been involved in a long-term

project to study various statistical aspects of the Google experiment.

We have been trying to gather the relevant data and information in

order to reconstruct and verify those parts of the Google experiment

that are based on classical computations (except when the required

computation is too heavy), and to perform a statistical analysis on

the data. This document describes the available data and information

for the Google experiment, some main questions in the evaluation of

the experiment, and some of our results and plans.

1 Introduction

The 2019 paper “Quantum supremacy using a programmable superconduct-

ing processor” [3] claimed that Google’s Sycamore quantum computer of 53

qubits and depth 20, performed a certain computation in about 200 seconds,

while a state-of-the-art classical supercomputer would take, according to the

Google team’s estimate, approximately 10,000 years to perform the same

computation. Google’s Sycamore quantum computer performed a sampling

task; that is, it generated random bitstrings of length 53, with considerable

noise, from a certain discrete probability distribution supported on all such

253 bitstrings. (Here, a bitstring refers to a vector with 0,1 entries.) The

arXiv:2210.12753v3 [quant-ph] 25 Jan 2023

speciﬁc sampling task performed by Google is referred to as random circuit

sampling (RCS, for short). Google’s announcement of quantum supremacy

was compared by various writers (see, e.g., [1]) to landmark technological

achievements such as the Wright brothers’ invention of a motor-operated air-

plane, the launching of Sputnik, and the landing of humans on the moon,

as well as to landmark scientiﬁc achievements such as Fermi’s demonstration

of a nuclear chain reaction, the discovery of the Higgs boson, and the LIGO

detection of gravitational waves.

In 2020 a team from the University of Science and Technology of China

(USTC) claimed [33] that the sampling task computed by their photonic

Jiuzhang quantum computer would take 2.5 billion years to perform on a

classical supercomputer. USTC’s quantum computer took about 200 seconds

to complete the task. This task is referred to as Gaussian boson sampling

(GBS, for short). In 2021, another team from USTC repeated the Google

RCS experiment with their Zuchongzhi quantum computer of 60 qubits and

depth 24 [32, 35], and claimed to achieve an even stronger form of quantum

advantage compared to the Google experiment.

The Google experiment represented a very large leap in various aspects

of the human ability to control noisy quantum systems. For example, the

previous experiment reported by the Google AI team used only nine qubits

[20]. This leap is especially impressive in terms of the dimensions of the

Hilbert space representing a state of the computer (from 100–500 dimensions

in [20] to 1016 dimensions in [3].)

Google’s quantum supremacy claim is based on two ingredients. The

ﬁrst ingredient is an assertion about the quality of the samples produced

by the quantum computer. This quality is described in terms of an impor-

tant parameter called the ﬁdelity. The second ingredient is an assertion

about the diﬃculty of achieving samples of the same quality by a clas-

sical supercomputer. The second assertion, and with it the entire quan-

tum supremacy claim, was largely refuted by research of several groups

[22, 21, 34, 12, 13, 23, 9] (among others) that exhibited classical algorithms

that are ten orders of magnitude faster than those used in the Google paper.

This was achieved, for example, by Pan, Chen, and Zhang [21] in 2021. Our

study concentrates on the ﬁrst claim dealing with the estimated ﬁdelity of

Google’s samples.

As we have already mentioned, the Google announcement was regarded

as a major scientiﬁc and technological breakthrough. On its own it gave some

evidence that the “strong Church–Turing thesis” had been violated and it

Figure 1: The price of bitcoin in USD in a period of 4 weeks around

9/23/2019. Source: CoinDesk

was described as an ironclad refutation of claims by some scientists (includ-

ing Kalai) that quantum computation is not possible. Of no less importance

is the fact that quantum supremacy was considered as a major intermedi-

ate step toward exhibiting experimentally quantum error-correction codes

needed for building larger quantum computers. The announcement of quan-

tum supremacy stirred a great deal of enthusiasm among scientists and in the

general public, and garnered signiﬁcant media attention. It had a substantial

impact; for example, following the media attention surrounding the leaking

of the quantum supremacy claims around September 22, 2019, the value of

bitcoin (and other digital currencies) sharply dropped by more than 10%

and it is a reasonable possibility that given the potential threat of quantum

computers to the safety of digital currencies, the quantum supremacy claims

caused this drop.

Scrutinizing the Google supremacy claim

The Google paper was brieﬂy posted on a NASA server and became publicly

available a month before it was published in October 2019. Following the

announcement of the quantum supremacy claim, the ﬁrst-named author (and

other researchers) raised various concerns about some aspects of the claims.

A few months later the authors initiated what has become a long-term project

to study various statistical aspects of the Google experiment. In particular,

we have been trying to gather the relevant data and information and to

reconstruct and verify those parts of the Google experiment that are based on

classical computations, except when the required computation is too heavy.

(We carried out some heavy computation on the cloud for which we put a cap

of 2000 dollars on our spending.) We also performed several “sanity tests”

of the experiment.

The structure of this paper

In Section 2 we provide a brief background on the Google experiment and

describe the various types of circuits used in the experiment. We also present

the chronology of the various Google experiments performed on the Sycamore

quantum computer leading to the ultimate quantum supremacy experiment,

as reported to us by the Google team. In Section 3 we describe the nature

of the calibration process. In Section 4 we describe the data requested from

the Google team, the data that was provided between October 2019 and

June 2022, and some other details related to the Google experiment and

other NISQ quantum supremacy experiments. In Section 5 we present two

proposals for future experiments. In Section 6 we discuss what we regard

as the main questions in the evaluation of the Google experiment and list

some conﬁrmations, refutations, concerns, and weaknesses, and in Section 7

we brieﬂy discuss where we are now in our study.

2 Google’s quantum supremacy claim

2.1 A brief background

In this paper we will assume knowledge of the Google experiment, Google’s

noise model, Google’s FXEB linear cross-entropy ﬁdelity estimator, and Google’s

Formula (77) in [4] for predicting the ﬁdelity of a circuit from the ﬁdelity of

its components. We will give here a brief summary of these topics.

The Google experiment is based on the building of a quantum computer

(circuit), with nsuperconducting qubits, that performs mrounds of compu-

tation. The computation is carried out by 1-qubit and 2-qubit gates. At the

end of the computation the qubits are measured, leading to a string of zeroes

and ones of length n. The ultimate experiment (on which Google’s central

claim was based) was for n= 53 and m= 20. It involved 1113 1-qubit gates

and 430 2-qubit gates. For that experiment the Google team produced a

sample of three million 0-1 vectors of length 53.

Every circuit Cwith nqubits describes a probability distribution PC(x)

for 0-1 vectors of length n. (In fact, it describes a 2n-dimensional vector

of complex amplitudes; for every 0-1 vector x, there is an associated ampli-

tude z(x) and PC(x) = |z(x)|2.) The quantum computer enables sampling

according to the probability distribution PC(x) with a considerable amount

of noise. When nand mare not too large, classical simulations enable com-

putation of the amplitudes themselves (and hence the probabilities PC(x)).

Google’s quantum supremacy claim is based on the fact that these classical

simulations quickly become infeasible as nand mgrow.

Google’s basic noise model for the noisy samples produced by their quan-

tum computer is

NC(x) = φPC+ (1 −φ)2−n,(1)

where φis the ﬁdelity, a parameter that roughly describes the quality of the

sample. (The ﬁdelity has a precise meaning in terms of the actual noisy

quantum process carried out by the quantum computer.)

Based on their noise model (and the fact that the distribution PCis an in-

stance of a Porter–Thomas distribution), the Google paper describes a statis-

tic called the linear cross-entropy estimator (denoted by FXEB .) Once the

quantum computer produces a sequence ˜x of Nsamples ˜x = (˜x(1),˜x(2),...,˜x(N)),

the following “linear cross-entropy” FXEB estimator of the ﬁdelity is com-

puted:

FXEB(˜x) = 1

i=1

2nPC(˜x(i))−1.(2)

Computing FXEB requires knowledge of PC(x) for sampled bitstrings.

The Google quantum supremacy claim is based also on the following a

priori prediction of the ﬁdelity of a circuit based on the probabilities of error

for the individual components:

φ=Y

g∈G1

(1 −eg)Y

g∈G2

(1 −eg)Y

q∈Q

(1 −eq).(3)

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

Google'sQuantumSupremacyClaim:Data,Documentation,andDiscussionGilKalai,YosefRinott,andTomerShohamJanuary26,2023AbstractInOctober2019,Naturepublishedapaper[3]describinganex-perimentthattookplaceatGoogle.Thepaperclaimstodemonstratequantum(computational)supremacyona53-qubitquantumcom-puter.SinceSeptemb...

展开>> 收起<<

Googles Quantum Supremacy Claim Data Documentation and Discussion Gil Kalai Yosef Rinott and Tomer Shoham.pdf

共32页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Googles Quantum Supremacy Claim Data Documentation and Discussion Gil Kalai Yosef Rinott and Tomer Shoham

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: