Evaluating thermal expectation values by almost ideal sampling with Trotter gates

TL;DR

This paper explores how applying Trotter gates to random phase product states enables efficient sampling for quantum many-body simulations at finite temperatures, especially in large systems with nonintegrable Hamiltonians.

Contribution

It demonstrates that Trotter gate-based sampling can achieve near-ideal efficiency in large systems, offering an alternative to traditional TPQ states for thermal calculations.

Findings

Sampling efficiency increases with system size for nonintegrable Hamiltonians.

Almost ideal sampling can be achieved in large systems with Trotter gates.

Chaotic Hamiltonian dynamics transform RPPSs into effective thermal states.

Abstract

We investigate the sampling efficiency for the simulations of quantum many-body systems at finite temperatures when initial sampling states are generated by applying Trotter gates to random phase product states (RPPSs). We restrict the number of applications of Trotter gates to be proportional to the system size, and thus the preparation would be easily accomplished in fault-tolerant quantum computers. When the Trotter gates are made from a nonintegrable Hamiltonian, we observe that the sampling efficiency increases with system size. This trend means that almost ideal sampling of initial states can be achieved in sufficiently large systems. We also find that the sampling efficiency is almost equal to that obtained by a typical pure quantum (TPQ) state method utilizing Haar random sampling in some cases. These findings suggest that chaotic Hamiltonian dynamics can transform RPPSs into an alternative to TPQ states for evaluating thermal expectation values.