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

Error mitigation is an essential component of achieving a practical quantum advantage in the near term, and a number of differ-ent approaches have been proposed. In this work, we recognize that many state-of-the-art error mitigation methods share a com-mon feature: they are data-driven, employ-ing classical data obtained from runs of dif-ferent 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 gen-eral data-driven error mitigation framework that we call UNIfied Technique for Error mit-igation with Data (UNITED). In certain sit-uations, 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 com-puter to benchmark UNITED, as well as other state-of-the-art methods, in mitigating observ-ables produced from random quantum cir-cuits 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 per-formance. For our largest considered shot bud-get (1010), we find that UNITED gives the most accurate mitigation. Hence, our work repre-sents a benchmarking of current error miti-gation methods and provides a guide for the regimes when certain methods are most use-ful.