Noise-resilient and resource-efficient hybrid algorithm for robust quantum gap estimation

TL;DR

This paper introduces a hybrid quantum algorithm for robustly estimating energy gaps in many-body systems, demonstrating resilience to various noise sources and resource efficiency on near-term quantum devices.

Contribution

The paper presents a novel hybrid quantum algorithm with proven noise resilience and error mitigation strategies for accurate gap estimation on noisy quantum hardware.

Findings

Algorithm is resilient to state preparation and measurement errors

Effective in mitigating mid-circuit depolarizing noise

Demonstrated successful implementation on IBM Quantum processors

Abstract

We present a hybrid quantum algorithm for estimating gaps in many-body energy spectra, supported by an analytic proof of its inherent resilience to state preparation and measurement errors, as well as mid-circuit multi-qubit depolarizing noise. Our analysis extends to a broader class of Markovian noise, employing error mitigation strategies that optimize the utilization of quantum resources. By integrating trial-state optimization and classical signal processing into the algorithm, we amplify the signal peak corresponding to the exact target gap beyond the error threshold, thereby significantly reducing gap estimate errors. The algorithm's robustness is demonstrated through noisy simulations on the Qiskit Aer simulator and demonstrations on IBM Quantum processors. These results underscore the potential to enable accurate quantum simulations on near-term noisy quantum devices without resource-intensive error correction.