Abstract: A method and system are disclosed for continuous optimization. The method comprises obtaining an optimization problem involving continuous or semi-continuous variables in a digital computer; initiating a stochastic search process in the digital computer in order to solve the optimization problem; until a stopping criterion is met constructing in the digital computer at least one stochastically generated polynomial in binary variables representative of choices of candidate future state of the stochastic search process, providing the at least one polynomial in binary variables to a binary sampling device, sampling from domains of the at least one polynomial in binary variables using the binary sampling device to generate binary sample points, receiving the generated binary sample points in the digital computer and transiting to next state of the stochastic search process and providing a best known solution found as a solution of the optimization problem using the digital computer.

Abstract: A method is disclosed for determining a minimum connected dominating set in a graph, the method comprising obtaining an indication of an input graph, the input graph comprising a plurality of nodes and a plurality of edges; generating a distance table comprising for each node of the input graph, an indication of a distance between the given node and each of the other node of the plurality of nodes; generating a corresponding constrained binary quadratic programming problem using the generated distance table; providing the corresponding constrained binary quadratic programming problem to a quantum annealing solver; obtaining at least one approximate solution from the quantum annealing solver; post-processing the at least one approximate solution and providing the post-processed at least one approximate solution.

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: The present disclosure provides methods, systems, and media for quantum computing, including allowing access to quantum ready and/or quantum enabled computers in a distributed computing environment (e.g., the cloud). Such methods and systems may provide optimization and computational services. Methods and systems of the present disclosure may enable quantum computing to be relatively and readily scaled across various types of quantum computers and users at various locations, in some cases without the need for users to have a deep understanding of the resources, implementation or the knowledge that may be required for solving optimization problems using a quantum computer. Systems provided herein may include user interfaces that enable users to perform data analysis in a distributed computing environment while taking advantage of quantum technology in the backend.

Abstract: The present disclosure provides methods, systems, and media for quantum computing, including allowing access to quantum ready and/or quantum enabled computers in a distributed computing environment (e.g., the cloud). Such methods and systems may provide optimization and computational services. Methods and systems of the present disclosure may enable quantum computing to be relatively and readily scaled across various types of quantum computers and users at various locations, in some cases without the need for users to have a deep understanding of the resources, implementation or the knowledge that may be required for solving optimization problems using a quantum computer. Systems provided herein may include user interfaces that enable users to perform data analysis in a distributed computing environment while taking advantage of quantum technology in the backend.

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

Abstract: The present disclosure provides methods, systems, and media for quantum computing, including allowing access to quantum ready and/or quantum enabled computers in a distributed computing environment (e.g., the cloud). Such methods and systems may provide optimization and computational services. Methods and systems of the present disclosure may enable quantum computing to be relatively and readily scaled across various types of quantum computers and users at various locations, in some cases without the need for users to have a deep understanding of the resources, implementation or the knowledge that may be required for solving optimization problems using a quantum computer. Systems provided herein may include user interfaces that enable users to perform data analysis in a distributed computing environment while taking advantage of quantum technology in the backend.

Abstract: A method and system are disclosed for solving a convex integer quadratic programming problem using a binary optimizer, the method comprising use of a processor for receiving a convex integer quadratic programming problem; converting the convex integer quadratic programming problem into a plurality of constrained and unconstrained binary quadratic programming problems and providing the plurality of unconstrained binary quadratic programming problems to the binary optimizer to thereby solve the convex integer quadratic programming problem.

Abstract: Described herein are methods, systems, and media for setting a system of superconducting qubits having a Hamiltonian representative of a polynomial on a bounded integer domain via bounded-coefficient encoding.

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.

Abstract: A method is disclosed for determining a minimum connected dominating set in a graph, the method comprising obtaining an indication of an input graph, the input graph comprising a plurality of nodes and a plurality of edges; generating a distance table comprising for each node of the input graph, an indication of a distance between the given node and each of the other node of the plurality of nodes; generating a corresponding constrained binary quadratic programming problem using the generated distance table; providing the corresponding constrained binary quadratic programming problem to a quantum annealing solver; obtaining at least one approximate solution from the quantum annealing solver; post-processing the at least one approximate solution and providing the post-processed at least one approximate solution.

Abstract: A method for solving the Lagrangian dual of a binary polynomially constrained polynomial programming problem comprises obtaining a binary polynomially constrained polynomial programming problem; until a convergence is detected, iteratively, providing a set of Lagrange multipliers, providing an unconstrained binary quadratic programming problem representative of the Lagrangian relaxation of the binary polynomially constrained polynomial programming problem at these Lagrange multipliers, providing the unconstrained binary quadratic programming problem to a quantum annealer, obtaining from the quantum annealer at least one corresponding solution, using the at least one corresponding solution to generate a new set of Lagrange multipliers; and providing all corresponding best-known primal-dual pairs and best-known feasible solutions after convergence.

Abstract: A method is disclosed for solving the Lagrangian dual of a constrained binary quadratic programming problem. The method comprises obtaining a constrained quadratic binary programming problem; until a convergence is detected, iteratively, performing a Lagrangian relaxation of the constrained quadratic binary programming problem to provide an unconstrained quadratic binary programming problem, providing the unconstrained quadratic binary programming problem to a quantum annealer, obtaining from the quantum annealer at least one corresponding solution, using the at least one corresponding solution to generate a new approximation for the Lagrangian dual bound; and providing a corresponding solution to the Lagrangian dual of the constrained binary quadratic programming problem after convergence.

Abstract: A method and system are disclosed for continuous optimization. The method comprises obtaining an optimization problem involving continuous or semi-continuous variables in a digital computer; initiating a stochastic search process in the digital computer in order to solve the optimization problem; until a stopping criterion is met constructing in the digital computer at least one stochastically generated polynomial in binary variables representative of choices of candidate future state of the stochastic search process, providing the at least one polynomial in binary variables to a binary sampling device, sampling from domains of the at least one polynomial in binary variables using the binary sampling device to generate binary sample points, receiving the generated binary sample points in the digital computer and transiting to next state of the stochastic search process and providing a best known solution found as a solution of the optimization problem using the digital computer.

Abstract: A method and system are disclosed for solving a convex integer quadratic programming problem using a binary optimizer, the method comprising use of a processor for receiving a convex integer quadratic programming problem; converting the convex integer quadratic programming problem into a plurality of constrained and unconstrained binary quadratic programming problems and providing the plurality of unconstrained binary quadratic programming problems to the binary optimizer to thereby solve the convex integer quadratic programming problem.