Estimating the error of an analog quantum simulator by additional measurements

TL;DR

This paper proposes a method to estimate the error in an analog quantum simulator caused by environmental decoherence by measuring additional correlators, demonstrated theoretically for a single spin system.

Contribution

It introduces a technique using extra measurements to verify the reliability of quantum simulations affected by known environmental perturbations.

Findings

Additional correlator measurements can verify simulation accuracy.

The method is theoretically demonstrated for a spin-boson system.

It enables error estimation without classical simulation of the quantum system.

Abstract

We study an analog quantum simulator coupled to a reservoir with a known spectral density. The reservoir perturbs the quantum simulation by causing decoherence. The simulator is used to measure an operator average, which cannot be calculated using any classical means. Since we cannot predict the result, it is difficult to estimate the effect of the environment. Especially, it is difficult to resolve whether the perturbation is small or if the actual result of the simulation is in fact very different from the ideal system we intend to study. Here, we show that in specific systems a measurement of additional correlators can be used to verify the reliability of the quantum simulation. The procedure only requires additional measurements on the quantum simulator itself. We demonstrate the method theoretically in the case of a single spin connected to a bosonic environment.