An iterative Bayesian variational quantum eigensolver with the von Mises-Fisher distribution
This work develops an iterative Bayesian quantum eigensolver to find a system's ground state vector by sequentially updating a von Mises-Fisher distribution based on measurements from a single ancilla qubit. It generalizes the method to handle multiple successful outcomes efficiently using a first-order expansion, proving that the convergence properties (monotonic overlap and concentration increase) are maintained within specific parameter ranges.