# Product Spectrum Ansatz and the Simplicity of Thermal States

## TL;DR

This paper introduces a variational quantum algorithm called the Product Spectrum Ansatz for efficiently preparing approximate thermal states and thermofield doubles on quantum computers, demonstrated on complex many-body models.

## Contribution

It proposes a new variational scheme for thermal state preparation that is simple, scalable, and effective for large quantum systems, including thermofield doubles.

## Key findings

- Efficient approximation of thermal states on quantum devices.
- Method works well for non-integrable models like the Ising chain and SYK model.
- Preparation of thermofield doubles extended to large systems.

## Abstract

Calculating the physical properties of quantum thermal states is a difficult problem for classical computers, rendering it intractable for most quantum many-body systems. A quantum computer, by contrast, would make many of these calculations feasible in principle, but it is still non-trivial to prepare a given thermal state or sample from it. It is also not known how to prepare special simple purifications of thermal states known as thermofield doubles, which play an important role in quantum many-body physics and quantum gravity. To address this problem, we propose a variational scheme to prepare approximate thermal states on a quantum computer by applying a series of two-qubit gates to a product mixed state. We apply our method to a non-integrable region of the mixed field Ising chain and the Sachdev-Ye-Kitaev model. We also demonstrate how our method can be easily extended to large systems governed by local Hamiltonians and the preparation of thermofield double states. By comparing our results with exact solutions, we find that our construction enables the efficient preparation of approximate thermal states on quantum devices. Our results can be interpreted as implying that the details of the many-body energy spectrum are not needed to capture simple thermal observables.