Multi-exponential Error Extrapolation and Combining Error Mitigation Techniques for NISQ Applications

TL;DR

This paper introduces multi-exponential error extrapolation for quantum error mitigation, providing rigorous proof and numerical validation, and combines it with other techniques to improve accuracy and reduce sampling costs in NISQ devices.

Contribution

It extends error extrapolation to multi-exponential forms, rigorously proves its effectiveness under Pauli noise, and develops methods to combine it with quasi-probability and symmetry verification techniques.

Findings

Multi-exponential extrapolation outperforms single-exponential in accuracy.

Combined methods reduce sampling costs significantly.

Numerical simulations validate the effectiveness of the proposed techniques.

Abstract

Noise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which requires large qubit overhead, we turn to quantum error mitigation, in which we make use of extra measurements. Error extrapolation is an error mitigation technique that has been successfully implemented experimentally. Numerical simulation and heuristic arguments have indicated that exponential curves are effective for extrapolation in the large circuit limit with an expected circuit error count around unity. In this article, we extend this to multi-exponential error extrapolation and provide more rigorous proof for its effectiveness under Pauli noise. This is further validated via our numerical simulations, showing orders of magnitude improvements in the estimation accuracy over single-exponential extrapolation. Moreover, we develop methods to combine error extrapolation with two other error mitigation techniques: quasi-probability and symmetry verification, through exploiting features of these individual techniques. As shown in our simulation, our combined method can achieve low estimation bias with a sampling cost multiple times smaller than quasi-probability while without needing to be able to adjust the hardware error rate as required in canonical error extrapolation.