Abstract: A method and a system are disclosed for solving a mixed-integer programming problem, the method comprising obtaining an indication of a mixed-integer programming optimization problem; until a performance criterion is met: providing the mixed-integer programming optimization problem to an optimization oracle adapted for solving the mixed-integer programming optimization problem using a feasibility pump technique and comprising an optimization solver, initializing parameters of an optimization oracle and an initial solution pair, the parameters comprising Monte-Carlo simulation parameters, a list of neighborhood functions and a measure of fractionality, and performing iterative calls to the optimization solver until a stopping condition is met; and providing at least one corresponding solution obtained from the optimization solver.

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 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 preprocessing a problem involving discrete optimization over a plurality of variables, the method comprising obtaining an indication of a problem involving discrete optimization; converting the problem involving discrete optimization into a problem suitable for a given optimization oracle architecture of an optimization oracle; providing a given number of times M the problem suitable for the given optimization oracle architecture to the optimization oracle; for each providing of the problem, performing a given number K of calls to the optimization oracle; each call generating a given configuration; obtaining a variable selection criterion, the variable selection criterion for determining at least one variable of the plurality of generated configurations that can be fixed; determining at least one variable that matches the variable selection criterion and a corresponding value for each variable; fixing the at least one determined variable at the corresponding value in the problem invo

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.