A digital quantum simulator in the presence of a bath

TL;DR

This paper establishes rigorous conditions under which a digital quantum simulator can accurately replicate a target system's dynamics even when coupled to a bath, challenging the notion that short cycle times are always necessary.

Contribution

It provides the first rigorous conditions for close simulation of open quantum systems across different regimes, replacing heuristic arguments with solid theoretical results.

Findings

Simulation can be accurate without extremely short cycle times.

Numerical examples support the theoretical conditions.

Broader regimes of simulation fidelity are explored.

Abstract

For a digital quantum simulator (DQS) imitating a target system, we ask the following question: Under what conditions is the simulator dynamics similar to that of the target in the presence of coupling to a bath? In this paper, we derive conditions for close simulation for three different physical regimes, replacing previous heuristic arguments on the subject with rigorous statements. In fact, we find that the conventional wisdom that the simulation cycle time should always be short for good simulation need not always hold up. Numerical simulations of two specific examples strengthen the evidence for our analysis, and go beyond to explore broader regimes.