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

Abstract

Error mitigation is an essential component of achieving 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 state-of-the-art methods, for problems with various numbers of qubits, circuit depths and total numbers of shots. We find that different techniques are optimal for different shot budgets. Namely, ZNE is the best performer for small shot budgets ($10^5$), while Clifford-based approaches are optimal for larger shot budgets ($10^6 - 10^8$), and for our largest considered shot budget ($10^{10}$), UNITED gives the most accurate correction. Hence, our work represents a benchmarking of current error mitigation methods, and provides a guide for the regimes when certain methods are most useful.Comment: 13 pages, 4 figure