Extending quantum probabilistic error cancellation by noise scaling

TL;DR

This paper introduces a unified quantum error mitigation framework combining probabilistic error cancellation and zero-noise extrapolation, enabling flexible noise scaling and hybrid techniques for improved quantum computation accuracy.

Contribution

It extends existing error mitigation methods by incorporating noise scaling, allowing for hybrid approaches and eliminating the need for detailed noise models.

Findings

Encompasses PEC and ZNE as special cases

Allows noise scaling without detailed noise models

Enables hybrid error mitigation strategies

Abstract

We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similarly to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device's noise model, e.g., avoiding gate set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), obtaining partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise reduction factors can be further post-processed with ZNE to better approximate the zero-noise limit.