Synergetic quantum error mitigation by randomized compiling and zero-noise extrapolation for the variational quantum eigensolver

Tomochika Kurita1, Hammam Qassim2, Masatoshi Ishii1, Hirotaka Oshima1, Shintaro Sato1, and Joseph Emerson2

1Quantum Laboratory, Fujitsu Research, Fujitsu Limited. 10-1 Morinosato-wakamiya, Atsugi, Kanagawa, Japan 243-0197
2Keysight Technologies Canada, 137 Glasgow St, Kitchener, ON, Canada, N2G 4X8

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We propose a quantum error mitigation strategy for the variational quantum eigensolver (VQE) algorithm. We find, via numerical simulation, that very small amounts of coherent noise in VQE can cause substantially large errors that are difficult to suppress by conventional mitigation methods, and yet our proposed mitigation strategy is able to significantly reduce these errors. The proposed strategy is a combination of previously reported techniques, namely randomized compiling (RC) and zero-noise extrapolation (ZNE). Intuitively, randomized compiling turns coherent errors in the circuit into stochastic Pauli errors, which facilitates extrapolation to the zero-noise limit when evaluating the cost function. Our numerical simulation of VQE for small molecules shows that the proposed strategy can mitigate energy errors induced by various types of coherent noise by up to two orders of magnitude.

When we execute quantum computations, it is crucial to minimize computational errors induced by hardware noise. For noisy intermediate-scale quantum (NISQ) hardware, quantum error mitigation techniques can be employed to reduce such errors. Addressing coherent noise, however, remains a significant challenge in error mitigation due to two reasons: (i) even a small amount of coherent noise can result in substantial computational errors, and (ii) these errors are difficult to mitigate using existing techniques.
In this work, we propose an error mitigation technique that effectively reduces errors induced by coherent noise. This technique utilizes synergetic effect of randomized compiling (RC) and zero-noise extrapolation (ZNE). RC converts coherent noise into stochastic Pauli noise, which can be effectively mitigated using ZNE. Our numerical simulations on variational quantum eigensolver algorithms demonstrate that our proposed mitigation technique exhibits a significant error-suppressing effect against coherent noise.

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Cited by

[1] Hugo Perrin, Thibault Scoquart, Alexander Shnirman, Jörg Schmalian, and Kyrylo Snizhko, "Mitigating crosstalk errors by randomized compiling: Simulation of the BCS model on a superconducting quantum computer", Physical Review Research 6 1, 013142 (2024).

[2] Nick S. Blunt, Laura Caune, Róbert Izsák, Earl T. Campbell, and Nicole Holzmann, "Statistical Phase Estimation and Error Mitigation on a Superconducting Quantum Processor", PRX Quantum 4 4, 040341 (2023).

[3] Ritajit Majumdar, Pedro Rivero, Friederike Metz, Areeq Hasan, and Derek S Wang, "Best practices for quantum error mitigation with digital zero-noise extrapolation", arXiv:2307.05203, (2023).

[4] Arnaud Carignan-Dugas, Shashank Kumar Ranu, and Patrick Dreher, "Estimating Coherent Contributions to the Error Profile Using Cycle Error Reconstruction", arXiv:2303.09945, (2023).

[5] Changwon Lee and Daniel K. Park, "Scalable quantum measurement error mitigation via conditional independence and transfer learning", Machine Learning: Science and Technology 4 4, 045051 (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-24 18:01:20) and SAO/NASA ADS (last updated successfully 2024-05-24 18:01:21). The list may be incomplete as not all publishers provide suitable and complete citation data.