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Scalable error mitigation for noisy quantum circuits produces competitive expectation values

Nature Physics volume 19, pages 752–759 (2023)Cite this article

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Abstract

Noise in existing quantum processors only enables an approximation to ideal quantum computation. However, for the computation of expectation values, these approximations can be improved by error mitigation. This has been experimentally demonstrated in small systems but the scaling of these methods to larger circuit volumes remains unknown. Here we demonstrate the utility of zero-noise extrapolation for practically relevant quantum circuits using up to 26 qubits, circuit depths of 120 and 1,080 CNOT gates. We study the scaling of the method for canonical examples of product states and entangling Clifford circuits of increasing size, and extend it to simulating the quench dynamics of two-dimensional Ising spin lattices with varying couplings. These experiments reveal that the accuracy of physically relevant observables after error mitigation substantially exceeds previously expected values. Furthermore, we show that the efficacy of error mitigation is greatly enhanced by additional error suppression techniques and native gate decomposition that reduce the circuit time. By combining these methods, the accuracy of our quantum simulation surpasses the classical approximations obtained from an established tensor network method. These results establish the potential of a useful quantum advantage using noisy, digital quantum processors.

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Fig. 1: Zero-noise extrapolation for short-depth quantum circuits.
Fig. 2: Scaling of zero-noise extrapolation for product states and entangling Clifford circuits.
Fig. 3: Quench dynamics of 2D Ising spin lattices: error-mitigated quantum simulation compared with PEPS.

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Data availability

Source data are available for this paper. All other data that support the plots within this Article and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank I. Lauer for contributions towards two-qubit gate calibration, and D. T. McClure and N. Sundaresan for valuable discussions on the device bring-up.

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Authors and Affiliations

  1. IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA

    Youngseok Kim, Christopher J. Wood, Theodore J. Yoder, Seth T. Merkel, Jay M. Gambetta, Kristan Temme & Abhinav Kandala

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Contributions

A.K. and K.T. designed the experiments. Y.K. and A.K. performed the experiments. C.J.W. and T.J.Y. ran the noisy simulations. S.T.M. provided the code for implementing Pauli twirling. K.T. ran the tensor network simulations. Y.K., C.J.W., T.J.Y., J.M.G., K.T. and A.K. analysed the data and wrote the paper.

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Correspondence to Youngseok Kim or Abhinav Kandala.

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Nature Physics thanks Xiao Yuan, Jinzhao Sun, Yukun Zhang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Sections I–VI, Figs. 1–10 and Table 1.

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Kim, Y., Wood, C.J., Yoder, T.J. et al. Scalable error mitigation for noisy quantum circuits produces competitive expectation values. Nat. Phys. 19, 752–759 (2023). https://doi.org/10.1038/s41567-022-01914-3

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