Abstract: The disclosed technology includes example embodiments that provide a framework for testing quantum programs in a manner similar to unit testing of classical programs by using a simulator that can predict the probability of measurements in a quantum system (known as a “strong simulator”). For a particular quantum program, embodiments of the disclosed technology use information exposed by strong simulation that would not otherwise be available to compare the given program to a desired reference program.

Abstract: Existing methods for dynamical simulation of physical systems use either a deterministic or random selection of terms in the Hamiltonian. In this application, example approaches are disclosed where the Hamiltonian terms are randomized and the precision of the randomly drawn approximation is adapted as the required precision in phase estimation increases. This reduces both the number of quantum gates needed and in some cases reduces the number of quantum bits used in the simulation.

Abstract: The disclosed technology concerns example embodiments for estimating eigenvalues of quantum operations using a quantum computer. Such estimations are useful in performing Shor's algorithm for factoring, quantum simulation, quantum machine learning, and other various quantum computing applications. Existing approaches to phase estimation are sub-optimal, difficult to program, require prohibitive classical computing, and/or require too much classical or quantum memory to be run on existing devices. Embodiments of the disclosed approach address one or more (e.g., all) of these drawbacks. Certain examples work by using a random walk for the estimate of the eigenvalue that (e.g., only) keeps track of the current estimate and the measurement record that it observed to reach that point.

Abstract: Existing methods for dynamical simulation of physical systems use either a deterministic or random selection of terms in the Hamiltonian. In this application, example approaches are disclosed where the Hamiltonian terms are randomized and the precision of the randomly drawn approximation is adapted as the required precision in phase estimation increases. This reduces both the number of quantum gates needed and in some cases reduces the number of quantum bits used in the simulation.

Abstract: The disclosed technology concerns example embodiments for estimating eigenvalues of quantum operations using a quantum computer. Such estimations are useful in performing Shor's algorithm for factoring, quantum simulation, quantum machine learning, and other various quantum computing applications. Existing approaches to phase estimation are sub-optimal, difficult to program, require prohibitive classical computing, and/or require too much classical or quantum memory to be run on existing devices. Embodiments of the disclosed approach address one or more (e.g., all) of these drawbacks. Certain examples work by using a random walk for the estimate of the eigenvalue that (e.g., only) keeps track of the current estimate and the measurement record that it observed to reach that point.

Abstract: The disclosed technology includes example embodiments that provide a framework for testing quantum programs in a manner similar to unit testing of classical programs by using a simulator that can predict the probability of measurements in a quantum system (known as a “strong simulator”). For a particular quantum program, embodiments of the disclosed technology use information exposed by strong simulation that would not otherwise be available to compare the given program to a desired reference program.

Abstract: Quantum methods for Bayesian inference represent prior or current posterior distributions with a series of qubits. A rotation gate defined by a rotation angle based on the prior or current posterior is applied to a selected qubit of the series. The selected qubit is measured, and if measurement is successful, the state of the series of qubits represents a posterior or updated posterior. If the measurement is unsuccessful, the representation of the prior or current posterior in the series of qubits, the rotation operation, and the measurement operations are repeated until success. A sinc2 based model distribution is obtained using a quantum Fourier transform (QFT), and, in some cases, a QFT is also used to implement convolution in a filtering operation for inference with time-dependent systems.

Abstract: Methods of training Boltzmann machines include rejection sampling to approximate a Gibbs distribution associated with layers of the Boltzmann machine. Accepted sample values obtained using a set of training vectors and a set of model values associate with a model distribution are processed to obtain gradients of an objective function so that the Boltzmann machine specification can be updated. In other examples, a Gibbs distribution is estimated or a quantum circuit is specified so at to produce eigenphases of a unitary.