Bayesian updating of a probability distribution encoded on a quantum register

Abstract

We investigate the problem of Bayesian updating of a probability distribution encoded in the quantum state of n qubits. The updating procedure takes the form of a quantum algorithm that prepares the quantum register in the state representing the posterior distribution. Depending on how the prior distribution is given, we describe two implementations, one probabilistic and one deterministic, of such an algorithm in the standard model of a quantum computer.