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 including one or more classical binary computers coupled to one or more quantum computers. The computing system is configured to process the one or more computing tasks including at least one combinatorial optimization task using a Filtering Variational Quantum Eigensolver (F-VQE) algorithm implemented by using one or more Ansätze circuits and a cost function arrangement to generate one or more quantum circuits in the quantum computer. The computing system iteratively applies a filtering operator to a cost function arrangement to generate a corresponding filtered cost function arrangement that excludes energy states that exceed an energy threshold and uses the filtered cost function arrangement in the one or more quantum circuits to generate output results.

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.