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

Abstract: A method and system for improving a stochastic control problem policy, the method including a sampling device obtaining data representing sample Boltzmann machine configurations, obtaining a stochastic control problem's initialization data and initial policy; assigning representative data of initial coupler weights and node biases and the Boltzmann machine's transverse field strength to the sampling device; until a stopping criterion is met, generating a present-epoch state-action pair, amending, sampling for the present-epoch state-action pair, approximating a present-epoch state-action Q-function value, obtaining a future-epoch state-action pair through a stochastic state process including a stochastic optimization test on all state-action pairs to provide the action at the future-epoch and update the future-epoch state's policy; amending the representative data, sampling for the future-epoch state-action pair, obtaining a future-epoch state-action Q-function value, updating each weight and bias and providi

Abstract: A method for estimating a thermodynamic property of a quantum Ising model with transverse field is disclosed.

Abstract: A quantum processor comprises a first set of qubits comprising a first plurality of substantially parallel qubits; a second set of qubits comprising N successive groups of a plurality of qubits (1, 2, . . . , N), wherein N is greater than or equal to two; wherein each group of qubits comprises a plurality of substantially parallel qubits; wherein each qubit of the first plurality of substantially parallel qubits of the first set of qubits crosses substantially perpendicularly a portion of the plurality of substantially parallel qubits of a first group of the second set of qubits; wherein each qubit of any given group of the second set of qubits crosses substantially perpendicularly a portion of the plurality of substantially parallel qubits of a successive group of the second set of qubits and a plurality of couplers, each coupler for providing a communicative coupling at a crossing of two qubits.

Abstract: A method for estimating a thermodynamic property of a quantum Ising model with transverse field is disclosed.

Abstract: A method and system are disclosed for improving a policy for a stochastic control problem, the stochastic control problem being characterized by a set of actions, a set of states, a reward structure as a function of states and actions, and a plurality of decision epochs, the method comprising using a sampling device obtaining data representative of sample configurations of a Boltzmann machine, obtaining initialization data and an initial policy for the stochastic control problem; assigning data representative of an initial weight and a bias of respectively each coupler and each node and the transverse field strength of the Boltzmann machine to the sampling device; until a stopping criterion is met generating a present-epoch state-action pair, amending data representative of none or at least one coupler and at least one bias, performing a sampling corresponding to the present-epoch state-action pair to obtain first sampling empirical means, obtaining an approximation of a value of a Q-function at the present-e

Abstract: A quantum processor comprises a first set of qubits comprising a first plurality of substantially parallel qubits; a second set of qubits comprising N successive groups of a plurality of qubits (1, 2, . . . , N), wherein N is greater than or equal to two; wherein each group of qubits comprises a plurality of substantially parallel qubits; wherein each qubit of the first plurality of substantially parallel qubits of the first set of qubits crosses substantially perpendicularly a portion of the plurality of substantially parallel qubits of a first group of the second set of qubits; wherein each qubit of any given group of the second set of qubits crosses substantially perpendicularly a portion of the plurality of substantially parallel qubits of a successive group of the second set of qubits and a plurality of couplers, each coupler for providing a communicative coupling at a crossing of two qubits.