Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach

TL;DR

This paper develops a framework to establish lower bounds on the quantum simulation cost for open quantum systems, using Lipschitz continuity, and demonstrates its effectiveness through examples.

Contribution

It introduces a novel Lipschitz continuity-based approach to determine lower bounds for simulating open quantum system dynamics, applicable to various quantum semigroups.

Findings

Lower bounds match upper bounds in several cases

Framework applies to both unital and non-unital dynamics

Convexified circuit depth quantifies simulation cost

Abstract

Simulating quantum dynamics is one of the most promising applications of quantum computers. While the upper bound of the simulation cost has been extensively studied through various quantum algorithms, much less work has focused on establishing the lower bound, particularly for the simulation of open quantum system dynamics. In this work, we present a general framework to calculate the lower bound for simulating a broad class of quantum Markov semigroups. Given a fixed accessible unitary set, we introduce the concept of convexified circuit depth to quantify the quantum simulation cost and analyze the necessary circuit depth to construct a quantum simulation scheme that achieves a specific order. Our framework can be applied to both unital and non-unital quantum dynamics, and the tightness of our lower bound technique is illustrated by showing that the upper and lower bounds coincide in several examples.