Noise-Assisted Variational Quantum Thermalization

Preparing 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 gate, 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 cost function for our variational algorithm. For a variety of Hamiltonians and system sizes, we 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 of temperatures for which the problem becomes harder. We hope that this first study on noise-assisted thermal state preparation will spark interest in future research on exploiting noise in variational algorithms.