Abstract: Embodiments of the present invention are directed to a hybrid quantum-classical (HQC) computer which includes a classical computer and a quantum computer. The HQC computer may perform a method in which: (A) the classical computer starts from a description of a initial problem and transforms the initial problem into a transformed problem of estimating an expectation value of a function of random variables; (B) the classical computer produces computer program instructions representing a Bayesian phase estimation scheme that solves the transformed problem; and (C) the hybrid quantum-classical computer executes the computer program instructions to execute the Bayesian phase estimation scheme, thereby producing an estimate of the expectation value of the function of random variables.