Unifying and benchmarking state-of-the-art quantum error mitigation techniques

Daniel Bultrini1,2, Max Hunter Gordon3, Piotr Czarnik1,4, Andrew Arrasmith1,5, M. Cerezo6,5, Patrick J. Coles1,5, and Lukasz Cincio1,5

1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
2Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, INF 229, D-69120 Heidelberg, Germany
3Instituto de Física Teórica, UAM/CSIC, Universidad Autónoma de Madrid, Madrid, Spain
4Institute of Theoretical Physics, Jagiellonian University, Krakow, Poland.
5Quantum Science Center, Oak Ridge, TN 37931, USA
6Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

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Error mitigation is an essential component of achieving a practical quantum advantage in the near term, and a number of different approaches have been proposed. In this work, we recognize that many state-of-the-art error mitigation methods share a common feature: they are data-driven, employing classical data obtained from runs of different quantum circuits. For example, Zero-noise extrapolation (ZNE) uses variable noise data and Clifford-data regression (CDR) uses data from near-Clifford circuits. We show that Virtual Distillation (VD) can be viewed in a similar manner by considering classical data produced from different numbers of state preparations. Observing this fact allows us to unify these three methods under a general data-driven error mitigation framework that we call UNIfied Technique for Error mitigation with Data (UNITED). In certain situations, we find that our UNITED method can outperform the individual methods (i.e., the whole is better than the individual parts). Specifically, we employ a realistic noise model obtained from a trapped ion quantum computer to benchmark UNITED, as well as other state-of-the-art methods, in mitigating observables produced from random quantum circuits and the Quantum Alternating Operator Ansatz (QAOA) applied to Max-Cut problems with various numbers of qubits, circuit depths and total numbers of shots. We find that the performance of different techniques depends strongly on shot budgets, with more powerful methods requiring more shots for optimal performance. For our largest considered shot budget ($10^{10}$), we find that UNITED gives the most accurate mitigation. Hence, our work represents a benchmarking of current error mitigation methods and provides a guide for the regimes when certain methods are most useful.

Current quantum computers face errors that pose challenges in surpassing the performance of the best classical computers. To fully harness the potential of quantum devices, it is crucial to correct these detrimental effects. Error mitigation methods are employed to address this issue. Among these methods, data-driven error mitigation stands out as a promising approach, involving classical post-processing of quantum measurement outcomes to rectify noise-induced effects. Various types of data have been utilized in this context, including noise strength scaling through Zero Noise Extrapolation (ZNE), data from near-Clifford circuits utilized by Clifford-data regression (CDR), and data obtained through Virtual Distillation (VD) by preparing multiple copies of a quantum state. To unify these approaches, we propose the UNIfied Technique for Error Mitigation with Data (UNITED), which integrates all these data types. Furthermore, we demonstrate that the unified method surpasses the individual components when sufficient quantum resources are available, employing a realistic noise model of a trapped ion quantum computer and two different types of quantum circuits with varying qubit counts and depths. Finally, we identify the most favorable conditions for different data-driven error mitigation methods.

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