Abstract: Methods and apparatus are provided that permit estimation of eigenphase or eigenvalue gaps in which random or pseudo-random unitaries are applied to a selected initial quantum state to produce a random quantum state. A target unitary is then applied to the random quantum state one or more times, or an evolution time is allowed to elapse after application of the target unitary. An inverse of the pseudo-random unitary used to produce the random quantum state is applied, and the resultant state is measured with respect to the initial quantum state. Measured values are used to produce Bayesian updates, and eigenvalue/eigenvector gaps are estimated. In some examples, the disclosed methods are used in amplitude estimate and control map determinations. Eigenvalue gaps for time-dependent Hamiltonians can be evaluated by adiabatic evolution of the Hamiltonian from an initial Hamiltonian to a final Hamiltonian.

Abstract: Methods and apparatus are provided that permit estimation of eigenphase or eigenvalue gaps in which random or pseudo-random unitaries are applied to a selected initial quantum state to produce a random quantum state. A target unitary is then applied to the random quantum state one or more times, or an evolution time is allowed to elapse after application of the target unitary. An inverse of the pseudo-random unitary used to produce the random quantum state is applied, and the resultant state is measured with respect to the initial quantum state. Measured values are used to produce Bayesian updates, and eigenvalue/eigenvector gaps are estimated. In some examples, the disclosed methods are used in amplitude estimate and control map determinations. Eigenvalue gaps for time-dependent Hamiltonians can be evaluated by adiabatic evolution of the Hamiltonian from an initial Hamiltonian to a final Hamiltonian.

Abstract: In some examples, techniques and architectures for solving combinatorial optimization or statistical sampling problems use a hierarchical approach. Such a hierarchical approach may be applied to a system or process in a patch-like fashion. A set of elements of the system correspond to a first tier. An objective function associates the set of elements with one another. The set of elements are partitioned into patches corresponding to a second tier. The patches individually include second tier elements that are subsets of the set of elements, and the individual patches have an energy configuration. The second tier elements of the patches are randomly initialized. Based, at least in part, on the objective function, a combinatorial optimization operation is performed on the second tier elements of the individual patches to modify the second tier elements of the individual patches.