Preparing quantum ensembles using mid-circuit measurements

Preparing a quantum-statistical ensemble on a quantum computer has application in many fields including simulating equilibrium physics, solving optimization problems, and training Boltzman machines. However, non-trivial ensembles cannot be prepared using unitary quantum gates alone. Therefore, we propose to prepare quantum ensembles by taking advantage of another resource available in quantum computing, quantum measurements. I will discuss the intimate relationship between quantum measurements and the entropy of a quantum statistical ensemble. Using mid-circuit quantum measurements, we are able to control the entropy of the quantum statistical ensemble, thereby, opening up the possibility to calculate the Helmholtz free energy of a simulated system.