Quantum Error Mitigation at the pre-processing stage

TL;DR

This paper introduces a pre-processing quantum error mitigation technique that uses tensor networks to reduce noise effects before measurement, outperforming traditional post-processing methods in efficiency and accuracy.

Contribution

It proposes a novel pre-processing approach using surrogate observables and tensor networks, significantly reducing classical computational complexity compared to existing methods.

Findings

Achieves near-theoretical lower measurement overhead

Reduces classical computation complexity by approximately 10^6 times

Outperforms Tensor Error Mitigation in error reduction and efficiency

Abstract

The realization of fault-tolerant quantum computers remains a challenging endeavor, forcing state-of-the-art quantum hardware to rely heavily on noise mitigation techniques. Standard quantum error mitigation is typically based on post-processing strategies. In contrast, the present work explores a pre-processing approach, in which the effects of noise are mitigated before performing a measurement on the output state. The main idea is to find an observable $Y$ such that its expectation value on a noisy quantum state $\mathcal{E(\rho)}$ matches the expectation value of a target observable $X$ on the noiseless quantum state $\rho$. Our method requires the execution of a noisy quantum circuit, followed by the measurement of the surrogate observable $Y$. The main enablers of our method in practical scenarios are Tensor Networks. The proposed method improves over Tensor Error Mitigation (TEM) in terms of average error, circuit depth, and complexity, attaining a measurement overhead that approaches the theoretical lower bound. The improvement in terms of classical computation complexity is in the order of $\sim 10^6$ times when compared to the post-processing computational cost of TEM in practical scenarios. Such gain comes from eliminating the need to perform the set of informationally complete positive operator-valued measurements (IC-POVM) required by TEM, as well as any other tomographic strategy.