Isometric tensor network representations of two-dimensional thermal states

TL;DR

This paper introduces an isometric tensor network approach using purification and imaginary-time evolution to efficiently simulate two-dimensional thermal states, offering a potentially less complex method for finite-temperature quantum systems.

Contribution

It presents a novel application of isometric tensor networks with purification for finite-temperature simulations in 2D, compatible with quantum computing implementations.

Findings

Efficient representation of thermal states of the transverse field Ising model.

Low computational complexity compared to existing methods.

Potential for implementation on quantum computers.

Abstract

Tensor networks provide a useful tool to describe low-dimensional complex many-body systems. Finding efficient algorithms to use these methods for finite-temperature simulations in two dimensions is a continuing challenge. Here, we use the class of recently introduced isometric tensor network states, which can also be directly realized with unitary gates on a quantum computer. We utilize a purification ansatz to efficiently represent thermal states of the transverse field Ising model. By performing an imaginary-time evolution starting from infinite temperature, we find that this approach offers a different way with low computational complexity to represent states at finite temperatures.