Fundamental limits of quantum error mitigation

Takagi, Ryuji; Endo, Suguru; Minagawa, Shintaro; Gu, Mile

doi:10.48550/arxiv.2109.04457

Cited by 15 publications

(27 citation statements)

References 55 publications

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“…Thus, NOX has runtime O(m 3 ) and is efficient in m. This result may seem to contradict Ref. [16], which shows that the EM protocols are fundamentally inefficient in the circuit depth. However, Ref.…”

Section: B Noiseless Output Extrapolationmentioning

confidence: 87%

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Efficiently improving the performance of noisy quantum computers

Ferracin¹,

Hashim²,

Ville³

et al. 2022

Preprint

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Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named "Noiseless Output Extrapolation" and "Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.

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Section: B Noiseless Output Extrapolationmentioning

confidence: 87%

“…). Thus, in general PEC (as well as all the other protocols based on quasi-probabilistic cancellation [16]) is inefficient due to the exponential scaling of the cost with the circuit depth. Nevertheless, if applied to circuits with depth m < ∼ ε −2 , PEC remains and efficient and practical solution.…”

Section: A Pauli Error Cancellationmentioning

confidence: 99%

Efficiently improving the performance of noisy quantum computers

Ferracin¹,

Hashim²,

Ville³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…An important question we leave open for future work is the extent to which noise affects the performance of our algorithm, and the degree to which error mitigation techniques [14], [43]- [47] can reduce the effects of the noise. Such an endeavor should take into consideration some recent theoretical and numerical work that have highlighted some limitations of quantum error mitigation on expectation estimation and training quantum circuits [48], [49].…”

Section: Discussionmentioning

confidence: 99%

Variational Quantum-Based Simulation of Waveguide Modes

Ewe,

Koh,

Goh

et al. 2021

Preprint

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Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a variational quantum algorithm in conjunction with the finite difference method for the calculation of propagation modes of an electromagnetic wave in a hollow metallic waveguide. The two-dimensional (2D) waveguide problem, described by the Helmholtz equation, is approximated by a system of linear equations, whose solutions are expressed in terms of simple quantum expectation values that can be evaluated efficiently on quantum hardware. Numerical examples are presented to validate the proposed method for solving 2D waveguide problems.

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“…Typically, errors in a quantum device are classified into quantum gate and measurement errors. For gate errors, numerous techniques have been designed such as zeronoise extrapolation [14,[19][20][21][22], probabilistic error cancellation [14,19,[23][24][25], subspace expansion [26,27], virtual distillation [28][29][30][31][32][33], learning-based method [34][35][36], and many others [37][38][39][40][41][42][43]. For measurement errors, the focus is not as much as that on gate errors though measurement errors are significantly larger than gate errors on many quantum platforms.…”

mentioning

confidence: 99%

Mitigating Quantum Errors via Truncated Neumann Series

Wang¹,

Chen²,

Wang³

2021

Preprint

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Quantum gates and measurements on quantum hardware are inevitably subject to hardware imperfections that lead to quantum errors. Mitigating such unavoidable errors is crucial to explore the power of quantum hardware better. In this paper, we propose a unified framework that can mitigate quantum gate and measurement errors in computing quantum expectation values utilizing the truncated Neumann series. The essential idea is to cancel the effect of quantum error by approximating its inverse via linearly combining quantum errors of different orders produced by sequential applications of the quantum devices with carefully chosen coefficients. Remarkably, the estimation error decays exponentially in the truncated order, and the incurred error mitigation overhead is independent of the system size, as long as the noise resistance of the quantum device is moderate. We numerically test this framework for different quantum errors and find that the computation accuracy is substantially improved. Our framework possesses several vital advantages: it mitigates quantum gate and measurement errors in a unified manner, it neither assumes any error structure nor requires the tomography procedure to completely characterize the quantum errors, and most importantly, it is scalable. These advantages empower our quantum error mitigation framework to be efficient and practical and extend the ability of near-term quantum devices to deliver quantum applications.

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Fundamental limits of quantum error mitigation

Cited by 15 publications

References 55 publications

Efficiently improving the performance of noisy quantum computers

Efficiently improving the performance of noisy quantum computers

Variational Quantum-Based Simulation of Waveguide Modes

Mitigating Quantum Errors via Truncated Neumann Series

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