Abstract: A quantum computing system includes a classical computer coupled in combination with a quantum computing system, wherein the quantum computing system is configurable to execute program instructions to process input data to generate corresponding output data. The quantum computing system is configured to execute a variational quantum amplitude estimation (VQAE) algorithm by iteratively executing a sequence of quantum operations including a maximum likelihood amplitude estimation and performing a variational approximation after an iteration to determine a variational quantum state associated with the outcome of the maximum likelihood amplitude estimation. The quantum computing system may also execute an adaptive VQAE by performing a rescaling process to reduce the variational cost of the VQAE.

Abstract: A computing system that includes a quantum computer, wherein the computing system is configured to use variational inference methods based on input data derived from an apparatus to be controlled, and to output data for controlling the operation of the apparatus. Methods for using the computing system for controlling operation of the apparatus. The computing system uses variational inference methods configured to drawing conclusion about unobserved variable given observations of related variables, to control the apparatus. The computing system may use Bayesian networks, quantum Born machines, adversarial objectives, or kernelized Stein discrepancy, to perform variational inference.