Dilution of error in digital Hamiltonian simulation

TL;DR

This paper demonstrates that in digital quantum simulations, noise can be independent of system size due to the dilution of errors, supported by analytic, numerical, and experimental evidence, and introduces an error mitigation method based on this phenomenon.

Contribution

It provides a microscopic explanation for error dilution in quantum simulations and proposes an error mitigation technique leveraging this effect.

Findings

Error in local observables can be independent of system size.

The 'relevant string length' explains when error dilution occurs.

Proposed error mitigation method improves scalability of noisy quantum simulations.

Abstract

We provide analytic, numerical and experimental evidence that the amount of noise in digital quantum simulation of local observables can be independent of system size in a number of situations. We provide a microscopic explanation of this dilution of errors based on the "relevant string length" of operators, which is the length of Pauli strings in the operator at time $s$ that belong to the exponentially small subspace of strings that can give a non-zero expectation value at time $t$. We show that this explanation can predict when dilution of errors occurs and when it does not. We propose an error mitigation method whose efficiency relies on this mechanism. Our findings imply that digital quantum simulation with noisy devices is in appropriate cases scalable in the sense that gate errors do not need to be reduced linearly to simulate larger systems.