Runtime-efficient zero-noise extrapolation from mixed physical and logical data

TL;DR

This paper introduces a hybrid zero-noise extrapolation method combining error-corrected and uncorrected quantum data, significantly reducing resource requirements for quantum error mitigation.

Contribution

It develops a mixed-data extrapolation strategy that leverages both physical and logical data points to improve zero-noise estimates and reduce runtime costs.

Findings

Mixed datasets lower variance in zero-noise estimates.

The method can reduce physical runtime by several orders of magnitude.

Applied to a six-spin Ising model, it outperforms pure error-corrected extrapolation.

Abstract

Partial quantum error correction and quantum error mitigation are expected to coexist in the pre-fault-tolerant regime, yet the resource advantage of combining them remains insufficiently quantified. We study zero-noise extrapolation constructed from mixed datasets that contain a small number of error-corrected data points together with data obtained without error correction. The low-noise logical points anchor the extrapolation, while the higher-noise physical points enlarge the noise baseline at a much smaller runtime cost. Under a simple model in which error correction suppresses the effective gate error rate from p to $\gamma$p, we derive the variance of the zero-noise estimator and compare the physical runtime required to reach a target precision. For Richardson extrapolation, the mixed-data strategy reduces variance amplification and can lower the required physical runtime by several orders of magnitude when $\gamma \leq 0.1$. As a proof of principle, we apply the method to digital quantum simulation of a six-spin transverse-field Ising model and find that mixed physical/logical datasets yield lower-variance zero-noise estimates and outperform extrapolation based only on error-corrected data in the parameter regime studied here. These results identify hybrid error correction and error mitigation as a practical route to resource-efficient quantum computation before full fault tolerance.