Ensemble-Based Quantum Signal Processing for Error Mitigation

TL;DR

This paper presents a noise-resilient quantum signal processing framework that mitigates coherent errors without increasing circuit complexity, enabling more reliable quantum algorithms on near-term hardware.

Contribution

It introduces an ensemble-based QSP approach that suppresses coherent errors and develops robust algorithms for key quantum applications, integrating error mitigation into algorithm design.

Findings

Suppresses random phase errors in Z rotations through measurement averaging

Enables implementation of polynomial functions of matrices with reduced noise impact

Provides a practical pathway for error mitigation in near-term quantum algorithms

Abstract

Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and fundamentally challenging noise source. We introduce a noise-resilient framework for Quantum Signal Processing (QSP) that mitigates such coherent errors without increasing circuit depth or ancillary qubit requirements. Our approach uses ensembles of noisy QSP circuits combined with measurement-level averaging to suppress random phase errors in Z rotations. Building on this framework, we develop robust QSP algorithms for implementing polynomial functions of Hermitian matrices and for estimating observables, with applications to Hamiltonian simulation, quantum linear systems, and ground-state preparation. We analyze the trade-off between approximation error and hardware noise, which is essential for practical implementation under the stringent depth and coherence constraints of current quantum hardware. Our results establish a practical pathway for integrating error mitigation seamlessly into algorithmic design, advancing the development of robust quantum computing, and enabling the discovery of scientific applications with near- and mid-term quantum devices.