Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Classically Spoofing System Linear Cross Entropy Score Benchmarking

Andrew Tanggara, Mile Gu, Kishor Bharti

TL;DR

The work challenges the robustness of existing quantum-supremacy benchmarks by showing a Pauli-path algorithm can efficiently approximate mQSVT outputs and refute the $sXQUATH$ conjecture for single-block circuits, while also spoofing the $sXES$ benchmark under noise. By leveraging Haar-random unitary moment matrices and Weingarten calculus, it derives conditions under which a polynomial-time classical estimator correlates with the true distribution, undermining the claimed hardness of spoofing. The results indicate that both Linear XEB and its system-level variant can be vulnerable to classical spoofing in realistic regimes, motivating the search for benchmarks with stronger, more general complexity-theoretic guarantees. Overall, the paper highlights the need for robust, cross-cutting benchmarks beyond XEB-type metrics to credibly certify quantum-supremacy demonstrations in the near term.

Abstract

In recent years, several experimental groups have claimed demonstrations of ``quantum supremacy'' or computational quantum advantage. A notable first claim by Google Quantum AI revolves around a metric called the Linear Cross Entropy Benchmarking (Linear XEB), which has been used in many quantum supremacy experiments since. The complexity-theoretic hardness of spoofing Linear XEB, however, depends on the Cross-Entropy Quantum Threshold (XQUATH) conjecture put forth by Aaronson and Gunn, which has been disproven for sublinear depth circuits. In the efforts on demonstrating quantum supremacy by quantum Hamiltonian simulation, a similar benchmarking metric called the System Linear Cross Entropy Score (sXES) holds firm in light of the aforementioned negative result due to its fundamental distinction with Linear XEB. Moreover, the complexity-theoretic hardness of spoofing sXES rests on the System Linear Cross-Entropy Quantum Threshold Assumption (sXQUATH), the formal relationship of which to XQUATH is unclear. Despite the promises offered by sXES for future demonstration of quantum supremacy, in this work we show that it can be classically simulated efficiently in certain regimes.

Classically Spoofing System Linear Cross Entropy Score Benchmarking

TL;DR

The work challenges the robustness of existing quantum-supremacy benchmarks by showing a Pauli-path algorithm can efficiently approximate mQSVT outputs and refute the conjecture for single-block circuits, while also spoofing the benchmark under noise. By leveraging Haar-random unitary moment matrices and Weingarten calculus, it derives conditions under which a polynomial-time classical estimator correlates with the true distribution, undermining the claimed hardness of spoofing. The results indicate that both Linear XEB and its system-level variant can be vulnerable to classical spoofing in realistic regimes, motivating the search for benchmarks with stronger, more general complexity-theoretic guarantees. Overall, the paper highlights the need for robust, cross-cutting benchmarks beyond XEB-type metrics to credibly certify quantum-supremacy demonstrations in the near term.

Abstract

In recent years, several experimental groups have claimed demonstrations of ``quantum supremacy'' or computational quantum advantage. A notable first claim by Google Quantum AI revolves around a metric called the Linear Cross Entropy Benchmarking (Linear XEB), which has been used in many quantum supremacy experiments since. The complexity-theoretic hardness of spoofing Linear XEB, however, depends on the Cross-Entropy Quantum Threshold (XQUATH) conjecture put forth by Aaronson and Gunn, which has been disproven for sublinear depth circuits. In the efforts on demonstrating quantum supremacy by quantum Hamiltonian simulation, a similar benchmarking metric called the System Linear Cross Entropy Score (sXES) holds firm in light of the aforementioned negative result due to its fundamental distinction with Linear XEB. Moreover, the complexity-theoretic hardness of spoofing sXES rests on the System Linear Cross-Entropy Quantum Threshold Assumption (sXQUATH), the formal relationship of which to XQUATH is unclear. Despite the promises offered by sXES for future demonstration of quantum supremacy, in this work we show that it can be classically simulated efficiently in certain regimes.
Paper Structure (16 sections, 3 theorems, 75 equations, 2 figures)

This paper contains 16 sections, 3 theorems, 75 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Spoofing mQSVT circuit benchmarking
  3. Pauli path algorithm
  4. Pauli Path Simulation for mQSVT Circuit
  5. Pauli Path Algorithm and Haar-random Unitary Moment Matrix
  6. Refuting sXQUATH
  7. Spoofing sXES benchmark
  8. Discussion
  9. Random Circuit Sampling Benchmark
  10. Hardness of classically spoofing mQSVT circuit benchmarking
  11. Reductions between threshold assumptions
  12. Haar-random unitary moment matrix
  13. Pauli path for mQSVT circuit
  14. Pauli path for single-block mQSVT circuit
  15. sXQUATH does not hold for single-block mQSVT circuit
  16. ...and 1 more sections

Key Result

Theorem 1

There exists an efficient classical algorithm taking an efficient description of $n+1$-qubit unitary $U$ with sublinear depth $d_U=o(n)$ and $n$ bit string $x$ as inputs and outputs an approximation $q(U,x)$ of a single-block mQSVT circuit output probability $p(U,x)$ that satisfies eqn. eqn:sxquath_

Figures (2)

  • Figure 1: mQSVT circuit $\mathtt{mQSVT}(U)$ where $U$ is a random $n+1$ qubit unitary made out of 2 qubit Haar-random unitaries and $R(\varphi)$ is $Z$-rotation gate with angle $\varphi$.
  • Figure 2: mQSVT circuit $\mathtt{mQSVT}(U)$ where $U$ is a random $n+1$ qubit unitary made out of 2 qubit Haar-random unitaries and $R(\varphi)$ is $Z$-rotation gate with angle $\varphi$.

Theorems & Definitions (12)

  • Theorem 1
  • Theorem 2
  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • ...and 2 more