Optimization of Algorithmic Errors in Analog Quantum Simulations

TL;DR

This paper develops a framework to quantify and analyze the errors in analog quantum simulations, focusing on device limitations and their impact on simulating many-body physics with Ising Hamiltonians.

Contribution

It introduces a general method for quantifying simulation errors and applies it to various time evolution techniques in analog quantum devices.

Findings

Errors from approximate time evolution are characterized.

Device constraints limit simulation accuracy.

Scaling of errors suggests ways to improve future device performance.

Abstract

Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using simulations on modern-day devices. Therefore, the inherent physical limitations of the device on the parameters of the simulation must be understood. This analysis examines the interplay of errors arising from simulation of approximate time evolution with those due to practical, real-world device constraints. These errors are studied in Heisenberg-type systems on analog quantum devices described by the Ising Hamiltonian. A general framework for quantifying these errors is introduced and applied to several proposed time evolution methods, including Trotter-like methods and Floquet-engineered constant-field approaches. The limitations placed on the accuracy of time evolution methods by current devices are discussed. Characterization of the scaling of coherent effects of different error sources provides a way to extend the presented Hamiltonian engineering methods to take advantage of forthcoming device capabilities.