Propagation of errors and quantitative quantum simulation with quantum advantage

TL;DR

This paper analyzes error propagation in analogue quantum simulators and identifies conditions under which current devices can achieve practical quantum advantage in simulating many-body dynamics beyond classical capabilities.

Contribution

It provides a detailed error analysis for analogue quantum simulators and establishes the hardware requirements for achieving quantum advantage in simulating complex many-body systems.

Findings

Current analogue simulators can reach regimes of practical quantum advantage.

Error propagation levels are quantified for Hubbard and transverse field Ising models.

Future fault-tolerant digital quantum computers require specific hardware improvements.

Abstract

The rapid development in hardware for quantum computing and simulation has led to much interest in problems where these devices can exceed the capabilities of existing classical computers and known methods. Approaching this for problems that go beyond testing the performance of a quantum device is an important step, and quantum simulation of many-body quench dynamics is one of the most promising candidates for early practical quantum advantage. We analyse the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods for analogue quantum simulators with neutral atoms in optical lattices and trapped ions. Considering the primary sources of error in analogue devices and how they propagate after a quench in studies of the Hubbard or long-range transverse field Ising model, we identify the level of error expected in quantities we extract from experiments. We conclude for models that are directly implementable that regimes of practical quantum advantage are attained in current experiments with analogue simulators. We also identify the hardware requirements to reach the same level of accuracy with future fault-tolerant digital quantum simulation. Verification techniques are already available to test the assumptions we make here, and demonstrating these in experiments will be an important next step.