Abstract: A method for improving an estimation of a property of a quantum state may include (a) using an interface of a digital computer to receive an indication of the property of the quantum state to be estimated; at least one quantum device; and at least one computational platform. The method may include using the at least one quantum device to obtain a plurality of measurement results of the quantum state. The method may include using the at least one computational platform to construct and train a neural network using the plurality of measurement results, wherein the neural network comprises at least one trainable parameter and wherein the neural network is representative of the quantum state. The method may include using the at least one computational platform and the property of the quantum state to train the at least one trainable parameter of the neural network to variationally improve the quantum state.

Abstract: A method is disclosed for estimating an expectation value of an observable of at least one target Hamiltonian using a base Hamiltonian, the method comprising obtaining an indication of a base Hamiltonian and an indication of an observable; setting a sampling device using the base Hamiltonian; obtaining from the sampling device a plurality of samples from a probability distribution defined by the base Hamiltonian; for each target Hamiltonian of a list of at least one target Hamiltonian: estimating an expectation value of the observable corresponding to the target Hamiltonian using the obtained plurality of samples from the probability distribution defined by the base Hamiltonian, the estimating comprising: computing a sample estimate of a ratio of partition functions of the target Hamiltonian and the base Hamiltonian, computing an unnormalized estimate for an expectation value of the observable with respect to the probability distribution defined by the target Hamiltonian, computing an estimate for an expectat