Noise-assisted variational quantum thermalization.

• DOI: 10.48550/arxiv.2111.03935
• Publication Date: 2022-03-09
• Authors: Jonathan Foldager; Arthur Pesah; Lars Kai Hansen
• Keywords: Quantum Physics; Science; Q; R; FOS: Physical sciences; Computational Physics (physics.comp-ph); 01 natural sciences; Article; 0103 physical sciences; Medicine; Quantum Physics (quant-ph); Physics - Computational Physics

AbstractPreparing thermal states on a quantum computer can have a variety of applications, from simulating many-body quantum systems to training machine learning models. Variational circuits have been proposed for this task on near-term quantum computers, but several challenges remain, such as finding a scalable cost-function, avoiding the need of purification, and mitigating noise effects. We propose a new algorithm for thermal state preparation that tackles those three challenges by exploiting the noise of quantum circuits. We consider a variational architecture containing a depolarizing channel after each unitary layer, with the ability to directly control the level of noise. We derive a closed-form approximation for the free-energy of such circuit and use it as a cost function for our variational algorithm. By evaluating our method on a variety of Hamiltonians and system sizes, we find several systems for which the thermal state can be approximated with a high fidelity. However, we also show that the ability for our algorithm to learn the thermal state strongly depends on the temperature: while a high fidelity can be obtained for high and low temperatures, we identify a specific range for which the problem becomes more challenging. We hope that this first study on noise-assisted thermal state preparation will inspire future research on exploiting noise in variational algorithms.