An introduction to Bayesian simulation-based inference for quantum machine learning with examples

Simulation is an indispensable tool in both engineering and the sciences. In simulation-based modeling, a parametric simulator is adopted as a mechanistic model of a physical system. The problem of designing algorithms that optimize the simulator parameters is the focus of the emerging field of simulation-based inference (SBI), which is often formulated in a Bayesian setting with the goal of quantifying epistemic uncertainty. This work studies Bayesian SBI that leverages a parameterized quantum circuit (PQC) as the underlying simulator. The proposed solution follows the well-established principle that quantum computers are best suited for the simulation of certain physical phenomena. It contributes to the field of quantum machine learning by moving beyond the likelihood-based methods investigated in prior work and accounting for the likelihood-free nature of PQC training. Experimental results indicate that well-motivated quantum circuits that account for the structure of the underlying physical system are capable of simulating data from two distinct tasks.