Universal Sampling Lower Bounds for Quantum Error Mitigation

TL;DR

This paper establishes fundamental lower bounds on the sampling cost for quantum error mitigation, showing that it must grow exponentially with circuit depth under various noise models, thus highlighting scalability challenges.

Contribution

It provides universal lower bounds on the sampling cost for quantum error mitigation applicable to all protocols, including nonlinear and future methods.

Findings

Sampling cost grows exponentially with circuit depth for many noise models.

Universal bounds apply to a broad class of mitigation protocols.

Fundamental obstacles to scalable quantum error mitigation are identified.

Abstract

Numerous quantum error-mitigation protocols have been proposed, motivated by the critical need to suppress noise effects on intermediate-scale quantum devices. Yet, their general potential and limitations remain elusive. In particular, to understand the ultimate feasibility of quantum error mitigation, it is crucial to characterize the fundamental sampling cost -- how many times an arbitrary mitigation protocol must run a noisy quantum device. Here, we establish universal lower bounds on the sampling cost for quantum error mitigation to achieve the desired accuracy with high probability. Our bounds apply to general mitigation protocols, including the ones involving nonlinear postprocessing and those yet-to-be-discovered. The results imply that the sampling cost required for a wide class of protocols to mitigate errors must grow exponentially with the circuit depth for various noise models, revealing the fundamental obstacles in the scalability of useful noisy near-term quantum devices.