© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2609.35535

Analysis of asymmetric errors in NISQ experiments

Gil Kalai, Tomer Shoham, Carsten Voelkmann

quant-phSubmitted Sep 28, 2026• Announced Sep 29, 2026• 0 citations

Abstract

This paper continues our analysis of NISQ experiments and especially the Google 2019 ``quantum supremacy" experiment. In arXiv:2008.05177 we proposed statistical tools to analyze symmetric and asymmetric readout errors, and the symmetric case was extensively developed and studied in arXiv:2404.00935, where we used Fourier methods combined with statistical tools. Here we extend and complement our earlier study and analyze asymmetric readout errors for data from experiments and simulations. Our study was further motivated by a paper by Fefferman et al. arXiv:2306.16659, who showed that the effect of amplitude damping gate errors is to have larger fractions of zeroes in the samples produced by the quantum computer. We show that this effect of gate errors is not observed in the Google experimental data, where, for the entire range of the number of qubits, $12 \le n \le 53$, the fraction of zeroes and ones reflects only the asymmetry of reported readout errors, and report on simulations with $n=12,14$ using IBM's and Google's simulators.

Comments: 29 pages, 6 figures, 10 tables

Related papers

Further Statistical Study of NISQ Experiments

Gil Kalai, Tomer Shoham, Carsten Voelkmann

We revisit and extend some topics that we studied in our previous works (Rinott, Kalai and Shoham 2022; Kalai, Rinott and Shoham, 2023,2024) regarding the Google 2019 "quantum supremacy" experiment. We extend our analysis of the prediction based on Google's digital error model (Formula (77)), based on more detailed data provided by Google. We also provide some preliminary analysis for a few other NISQ experiments.

quant-pharXiv:2512.10722•Dec 12, 2025•0 citations

Random Circuit Sampling: Fourier Expansion and Statistics

Gil Kalai, Yosef Rinott, Tomer Shoham

Considerable effort in experimental quantum computing is devoted to noisy intermediate scale quantum computers (NISQ computers). Understanding the effect of noise is important for various aspects of this endeavor including notable claims for achieving quantum supremacy and attempts to demonstrate quantum error correcting codes. In this paper we use Fourier methods combined with statistical analysis to study the effect of noise. In particular, we use Fourier analysis to refine the linear cross-entropy fidelity estimator. We use both analytical methods and simulations to study the effect of readout and gate errors, and we use our analysis to study the samples of Google's 2019 quantum supremacy experiment.

arXiv:2404.00935•Apr 1, 2024•0 citations

Google's Quantum Supremacy Claim: Data, Documentation, and Discussion

Gil Kalai, Yosef Rinott, Tomer Shoham

In October 2019, Nature published a paper describing an experiment that took place at Google. The paper claims to demonstrate quantum (computational) supremacy on a 53-qubit quantum computer. 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.

arXiv:2210.12753•Oct 23, 2022•3 citations

Questions and Concerns About Google's Quantum Supremacy Claim

Gil Kalai, Yosef Rinott, Tomer Shoham

In October 2019, Nature published a paper [6] describing an experimental work that was performed at Google. The paper claims to demonstrate quantum (computational) supremacy on a 53-qubit quantum computer. Since then we have been involved in a long-term project to study various statistical aspects of the Google experiment. In [30] we studied Google's statistical framework that we found to be very sound and offered some technical improvements. This document describes three main concerns (based on statistical analysis) about the Google 2019 experiment. The first concern is that the data do not agree with Google's noise model (or any other specific model). The second concern is that a crucial simple formula for a priori estimation of the fidelity seems to involve an unexpected independence assumption, and yet it gives very accurate predictions. The third concern is about statistical properties of the calibration process.

arXiv:2305.01064•May 1, 2023•1 citation

TQEA: Temporal Quantum Error Analysis

Betis Baheri, Daniel Chen, Bo Fang +6 more

The growth of need of quantum computers in many domains such as machine learning, numerical scientific simulation and finance has urged the quantum computers to produce more stable and less error-prone results. However, to mitigate the impact of the noise inside each quantum device remains a present challenge. In this paper, we investigate the temporal behavior of noisy intermediate-scale quantum (NISQ) computer errors based on calibration data and the characteristics of individual devices. In particular, we collect calibration data of IBM-Q machines over 90 days and compare the quantum error robustness across processor types, quantum topology and quantum volumes. We analyze the aging effect by comparing the quantum error data from four IBM quantum computers during 2019-2021 showing that only one computer experienced significant error growth overtime. In this study, we simply analyze the collected data and run temporal test analysis to observe the behaviour of IBM-Q computers.

IEEE/IFIP International Conference on Dependable Systems and Networks - Supplemental Volume (DSN-S)•Jun 1, 2021•8 citations

Reproducibility in Quantum Computing

Samudra Dasgupta, Travis S. Humble

Reproducibility is important for validating the performance of applications in quantum computing as a measure of consistency in computation. Current noisy, intermediate-scale devices quantum (NISQ) devices are strongly affected by intrinsic noise that leads to a variety of computational error mechanisms. Here we assess reproducibility of NISQ computing by focusing on a specific simple error mechanism that arises during noisy readout. Using an asymmetric channel for binary readout, we develop an analytic bound on the Hellinger distance between computational outputs for different readout parameters. We validate this model using characterization and testing of the IBM toronto device, which displays a range of readout parameters. We find that to ensure reproducibility, one must avoid using register elements characterized by fidelity asymmetry exceeding a threshold.

IEEE Computer Society Annual Symposium on VLSI•Jul 1, 2021•6 citations

This paper continues our analysis of NISQ experiments and especially the Google 2019 ``quantum supremacy" experiment. In arXiv:2008.05177 we proposed statistical tools to analyze symmetric and asymmetric readout errors, and the symmetric case was extensively developed and studied in arXiv:2404.00935, where we used Fourier methods combined with statistical tools.

Here we extend and complement our earlier study and analyze asymmetric readout errors for data from experiments and simulations.

Our study was further motivated by a paper by Fefferman et al. arXiv:2306.16659, who showed that the effect of amplitude damping gate errors is to have larger fractions of zeroes in the samples produced by the quantum computer. We show that this effect of gate errors is not observed in the Google experimental data, where, for the entire range of the number of qubits,

12 \le n \le 53

, the fraction of zeroes and ones reflects only the asymmetry of reported readout errors, and report on simulations with

n=12,14

using IBM's and Google's simulators.

Considerable effort in experimental quantum computing is devoted to noisy intermediate scale quantum computers (NISQ computers). Understanding the effect of noise is important for various aspects of this endeavor including notable claims for achieving quantum supremacy and attempts to demonstrate quantum error correcting codes. In this paper we use Fourier methods combined with statistical analysis to study the effect of noise. In particular, we use Fourier analysis to refine the linear cross-entropy fidelity estimator. We use both analytical methods and simulations to study the effect of readout and gate errors, and we use our analysis to study the samples of Google's 2019 quantum supremacy experiment.

In October 2019, Nature published a paper describing an experiment that took place at Google. The paper claims to demonstrate quantum (computational) supremacy on a 53-qubit quantum computer. 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.

In October 2019, Nature published a paper [6] describing an experimental work that was performed at Google. The paper claims to demonstrate quantum (computational) supremacy on a 53-qubit quantum computer. Since then we have been involved in a long-term project to study various statistical aspects of the Google experiment. In [30] we studied Google's statistical framework that we found to be very sound and offered some technical improvements. This document describes three main concerns (based on statistical analysis) about the Google 2019 experiment. The first concern is that the data do not agree with Google's noise model (or any other specific model). The second concern is that a crucial simple formula for a priori estimation of the fidelity seems to involve an unexpected independence assumption, and yet it gives very accurate predictions. The third concern is about statistical properties of the calibration process.

The growth of need of quantum computers in many domains such as machine learning, numerical scientific simulation and finance has urged the quantum computers to produce more stable and less error-prone results. However, to mitigate the impact of the noise inside each quantum device remains a present challenge. In this paper, we investigate the temporal behavior of noisy intermediate-scale quantum (NISQ) computer errors based on calibration data and the characteristics of individual devices. In particular, we collect calibration data of IBM-Q machines over 90 days and compare the quantum error robustness across processor types, quantum topology and quantum volumes. We analyze the aging effect by comparing the quantum error data from four IBM quantum computers during 2019-2021 showing that only one computer experienced significant error growth overtime. In this study, we simply analyze the collected data and run temporal test analysis to observe the behaviour of IBM-Q computers.

Reproducibility is important for validating the performance of applications in quantum computing as a measure of consistency in computation. Current noisy, intermediate-scale devices quantum (NISQ) devices are strongly affected by intrinsic noise that leads to a variety of computational error mechanisms. Here we assess reproducibility of NISQ computing by focusing on a specific simple error mechanism that arises during noisy readout. Using an asymmetric channel for binary readout, we develop an analytic bound on the Hellinger distance between computational outputs for different readout parameters. We validate this model using characterization and testing of the IBM toronto device, which displays a range of readout parameters. We find that to ensure reproducibility, one must avoid using register elements characterized by fidelity asymmetry exceeding a threshold.