Performance and scaling analysis of variational quantum simulation

TL;DR

This paper empirically analyzes how the minimal quantum circuit depth scales in variational quantum simulation, showing potential advantages over Trotterized methods for certain system sizes and times.

Contribution

It provides a comparative scaling analysis of VQS versus Trotterization, highlighting conditions where VQS may be more efficient.

Findings

VQS shows better scaling of circuit depth than Trotterization.

VQS potentially offers advantages in specific system sizes and evolution times.

Classical complexity considerations are discussed in relation to VQS performance.

Abstract

We present an empirical analysis of the scaling of the minimal quantum circuit depth required for a variational quantum simulation (VQS) method to obtain a solution to the time evolution of a quantum system within a predefined error tolerance. In a comparison against a non-variational method based on Trotterized time evolution, we observe a better scaling of the depth requirements using the VQS approach with respect to both the size of the system and the simulated time. Results are also put into perspective by discussing the corresponding classical complexity required for VQS. Our results allow us to identify a possible advantage region for VQS over Trotterization.