Scalable Evaluation of Quantum-Circuit Error Loss Using Clifford Sampling

Wang, Zhen; Chen, Yanzhu; Song, Zixuan; Qin, Dayue; Li, Hekang; Guo, Qiujiang; Wang, H.; Song, Cunxian; Liu, Ying

doi:10.1103/physrevlett.126.080501

Cited by 6 publications

(4 citation statements)

References 62 publications

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“…( 47) is a homogeneous polynomial of degree 2 in matrix elements of the single-qubit gates in the circuits. Since the Clifford group is a unitary 2-design, the loss function satisfies L C ð ⃗ θÞ ¼ L U ð ⃗ θÞ (Wang, Chen et al, 2021). Therefore, by training over the Clifford circuits and minimizing L C ð ⃗ θÞ, we are minimizing the errors in the more general unitary circuits in U.…”

Section: H Learning-based Methodsmentioning

confidence: 99%

Quantum error mitigation

Cai,

Babbush,

Benjamin

et al. 2023

Rev. Mod. Phys.

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138

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For quantum computers to successfully solve real-world problems, it is necessary to tackle the challenge of noise: the errors that occur in elementary physical components due to unwanted or imperfect interactions. The theory of quantum fault tolerance can provide an answer in the long term, but in the coming era of noisy intermediate-scale quantum machines one must seek to mitigate errors rather than completely eliminate them. This review surveys the diverse methods that have been proposed for quantum error mitigation, assesses their in-principle efficacy, and describes the hardware demonstrations achieved to date. Commonalities and limitations among the methods are identified, while mention is made of how mitigation methods can be chosen according to the primary type of noise present, including algorithmic errors. Open problems in the field are identified, and the prospects for realizing mitigation-based devices that can deliver a quantum advantage with an impact on science and business are discussed.

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Section: H Learning-based Methodsmentioning

confidence: 99%

Quantum error mitigation

Cai,

Babbush,

Benjamin

et al. 2023

Rev. Mod. Phys.

Self Cite

138

View full text Add to dashboard Cite

show abstract

“…The efficacy of Clifford learning lies upon two results. This first result is that we can evaluate quantum-circuit error loss by sampling Clifford circuits [70] when the error model is independent of single-qubit gates. The underlying reason is that Clifford circuits formulate a unitary-2 design, [71] hence we have…”

Section: Error Mitigation Using Clifford-circuit Learningmentioning

confidence: 99%

“…( 58) does not hold in general. However we can still obtain a reliable estimation of the loss over unitary circuits using the method of hybrid sampling, [70] where a few gates in the circuit can be general unitaries while the other gates are all Clifford.…”

Section: Error Mitigation Using Clifford-circuit Learningmentioning

confidence: 99%

An overview of quantum error mitigation formulas

Qin

Xu²,

Liu³

2022

Chinese Phys. B

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Minimizing the effect of noise is essential for quantum computers. The conventional method to protect qubits against noise is through quantum error correction. However, for current quantum hardware in the so-called noisy intermediate-scale quantum (NISQ) era, noise presents in these systems and is too high for error correction to be beneficial. Quantum error mitigation is a set of alternative methods for minimizing errors, including error extrapolation, probabilistic error cancellation, measurement error mitigation, subspace expansion, symmetry verification, virtual distillation, etc. The requirement for these methods is usually less demanding than error correction. Quantum error mitigation is a promising way of reducing errors on NISQ quantum computers. This paper gives a comprehensive introduction to quantum error mitigation. The state-of-art error mitigation methods are covered and formulated in a general form, which provides a basis for comparing, combining and optimizing different methods in future work.

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“…Compared with the first category, the successful implementation of a constraint-based approach does not rely on error model benchmarking, e.g. gate set tomography [17][18][19][20] and sampling trial circuits [21][22][23]. Recently, virtual distillation protocols are proposed for error mitigation, exploring the universal constraint that the error-free state is a pure state [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Dual-state purification for practical quantum error mitigation

Huo,

2021

Preprint

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Quantum error mitigation is essential for computing on the noisy quantum computer with a limited number of qubits. In this paper, we propose a practical protocol of error mitigation by virtually purifying the quantum state without qubit overhead or requiring only one ancillary qubit. In dual-state purification, we effectively generate a purified state with increased fidelity using the erroneous state and its dual state, respectively, prepared with the noisy quantum circuit and the dual map of its inverse circuit. Combined with tomography purification, we can make sure that the final estimate of an observable is obtained from a pure state. The numerical result suggests that our protocol reduces the error by a rescaling factor decreasing with the qubit number and circuit depth, i.e. the performance of purification is better for larger circuits. On a cloud quantum computer, we successfully demonstrate the reduced error with a quantum variational eigensolver circuit.

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Scalable Evaluation of Quantum-Circuit Error Loss Using Clifford Sampling

Cited by 6 publications

References 62 publications

Quantum error mitigation

Quantum error mitigation

An overview of quantum error mitigation formulas

Dual-state purification for practical quantum error mitigation

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