  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 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.
