Algorithmic error mitigation for quantum eigenvalues estimation

TL;DR

This paper introduces an error mitigation method for quantum eigenvalue estimation that significantly reduces algorithmic errors without increasing circuit complexity, making it feasible for early fault-tolerant quantum devices.

Contribution

The authors propose a polynomial-resource error mitigation strategy that suppresses algorithmic errors to any order in quantum eigenvalue estimation.

Findings

Achieves several orders of magnitude error reduction in practical cases

Number of observables grows polynomially with Hamiltonian terms

Method enables accurate eigenvalue estimation on limited-resource quantum devices

Abstract

When estimating the eigenvalues of a given observable, even fault-tolerant quantum computers will be subject to errors, namely algorithmic errors. These stem from approximations in the algorithms implementing the unitary passed to phase estimation to extract the eigenvalues, e.g. Trotterisation or qubitisation. These errors can be tamed by increasing the circuit complexity, which may be unfeasible in early-stage fault-tolerant devices. Rather, we propose in this work an error mitigation strategy that enables a reduction of the algorithmic errors up to any order, at the cost of evaluating the eigenvalues of a set of observables implementable with limited resources. The number of required observables is estimated and is shown to only grow polynomially with the number of terms in the Hamiltonian, and in some cases, linearly with the desired order of error mitigation. Our results show error reduction of several orders of magnitude in physically relevant cases, thus promise accurate eigenvalue estimation even in early fault-tolerant devices with limited number of qubits.