Qubit-efficient simulation of thermal states with quantum tensor networks

TL;DR

This paper introduces a quantum algorithm that efficiently simulates thermal states of many-body systems using fewer qubits by leveraging tensor network techniques and variational optimization, demonstrated on a trapped-ion quantum processor.

Contribution

It proposes a novel holographic quantum simulation method for thermal states that requires only a cross-sectional qubit count, combining quantum tensor networks with variational optimization.

Findings

Successfully demonstrated on a trapped-ion quantum processor with minimal qubits.

Classical simulations reveal the relationship between circuit complexity and accuracy.

The method effectively simulates thermal properties over a wide temperature range.

Abstract

We present a holographic quantum simulation algorithm to variationally prepare thermal states of $d$-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a ($d$-1)-dimensional cross-section. This technique implements the thermal state by approximately unraveling the quantum matrix-product density operator (qMPDO) into a stochastic mixture of quantum matrix product states (sto-qMPS). The parameters of the quantum circuits generating the qMPS and of the probability distribution generating the stochastic mixture are determined through a variational optimization procedure. We demonstrate a small-scale proof of principle demonstration of this technique on Quantinuum's trapped-ion quantum processor to simulate thermal properties of correlated spin-chains over a wide temperature range using only a single pair of hardware qubits. Then, through classical simulations, we explore the representational power of two versions of sto-qMPS ansatzes for larger and deeper circuits and establish empirical relationships between the circuit resources and the accuracy of the variational free-energy.