Data-driven adaptive quantum error mitigation for probability distribution

TL;DR

The paper addresses the problem of reliably reconstructing error-mitigated probability distributions from noisy quantum runs by introducing two adaptive QEM-selection protocols: N-version programming, which filters out outlier distributions among multiple QEM strategies using total-variation distance, and a consistency-based method, which selects the extrapolation approach with the smallest variance across many data-point combinations. These methods are validated on a Trotterized transverse-field Ising model circuit, demonstrating robust outlier rejection and per-bin extrapolation consistency, thereby enabling more trustworthy distribution estimates in NISQ-era quantum computing. The work highlights practical implications for applying QEM to distribution-based tasks beyond single-observable expectations and discusses extensions to probabilistic error cancellation and integration with quantum error correction. Overall, the proposed framework offers a principled, software-engineering-inspired route to optimize QEM for probability distributions in realistic hardware scenarios.

Abstract

Quantum error mitigation (QEM) has been proposed as a class of hardware-friendly error suppression techniques. While QEM has been primarily studied for mitigating errors in the estimation of expectation values of observables, recent works have explored its application to estimating noiseless probability distributions. In this work, we propose two protocols to improve the accuracy of QEM for probability distributions, inspired by techniques in software engineering. The first is the N-version programming method, which compares probability distributions obtained via different QEM strategies and excludes the outlier distribution, certifying the feasibility of the error-mitigated distributions. The second is a consistency-based method for selecting an appropriate extrapolation strategy. Specifically, we prepare $K$ data points at different error rates, choose $L<K$ of them for extrapolation, and evaluate error-mitigated results for all $\binom{K}{L}$ possible choices. We then select the extrapolation method that yields the smallest variance in the error-mitigated results. This procedure can also be applied bitstring-wise, enabling adaptive error mitigation for each probability in the distribution.

Figures (4)

• Figure 1: The N-version programming approach calculates the distances among the distributions of the given QEM methods (QEMs A to D in this figure) and effectively identifies the method that deviates most from the majority (in this case, QEM D).
• Figure 2: The consistency-based method. In this approach, we hypothesize that when the optimal QEM method is employed, the mitigation results remain almost unchanged regardless of which data points are used. Under this assumption, the method that yields the smallest variance in QEM results across different data points is regarded as the most "consistent", and thus identified as the optimal one.
• Figure 3: An example of a 3-qubit Trotterized circuit for the one-dimensional transverse-field Ising model. A single block composed of RX, RZ, and CNOT gates is repeatedly applied for $M$ times. We used Qiskit qiskit2024 to draw the circuit.
• Figure 4: Count of the N-version-programming method’s ranks among QEM methods sorted by the corresponding TVDs. The N-version programming method is never ranked 4th for any parameter $M$, indicating that the method identifies the outlier as depicted in Fig. \ref{['fig: N-version programming method']}.