Abstract: A method for solving an integer or a mixed-integer programming problem may include: (a) obtaining an indication of a quantum Hamiltonian representative of an integer or a mixed-integer programming problem; (b) implementing the quantum Hamiltonian on a quantum optical device, wherein the quantum optical device comprises quantum gates; (c) using the quantum optical device to prepare a quantum state of the system of qumodes; (d) performing a measurement of the system of the qumodes; and (e) providing a solution of the integer or the mixed-integer programming problem based on the measurement.

Abstract: The present disclosure may include methods, devices, and systems for constructing a routed circuit to allocate information qubits. The routed circuit may comprise at least one two-qubit gate and zero or more one-qubit gates on a quantum chip structure represented by a graph comprising vertices and edges.

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: The present disclosure provides methods and systems for solving problems. Examples of problems include, but are not limited to, maximum clique problems.

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 for improving an estimation of a property of a quantum state may include (a) using an interface of a digital computer to receive an indication of the property of the quantum state to be estimated; at least one quantum device; and at least one computational platform. The method may include using the at least one quantum device to obtain a plurality of measurement results of the quantum state. The method may include using the at least one computational platform to construct and train a neural network using the plurality of measurement results, wherein the neural network comprises at least one trainable parameter and wherein the neural network is representative of the quantum state. The method may include using the at least one computational platform and the property of the quantum state to train the at least one trainable parameter of the neural network to variationally improve the quantum state.

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 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: The present disclosure provides methods and systems for using one or more artificial intelligence (AI) procedures (such as one or more machine learning (ML) or reinforcement learning (RL) procedures) implemented on a classical computer to perform a heuristic through interaction with a computation performed using a classical or non-classical computer (such as a quantum computer).

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 computing system and a method are disclosed for enabling a processing device to remotely access a computing platform over a network, wherein the computing platform comprises at least one physics-inspired computer simulator comprising tunable parameters, the computing system comprising a communications interface configured to receive a request, wherein the request comprises at least one computational task to process using at least one physics-inspired computer simulator comprising tunable parameters; a control unit operatively connected to the communications interface and to the at least one physics-inspired computer simulator comprising tunable parameters, the control unit configured to translate the request into instructions for the at least one physics-inspired computer simulator deliver the instructions to the at least one physics-inspired computer simulator to perform the at least one computational task, receive at least one corresponding solution; and a memory operatively connected to the to the contro

Abstract: The present disclosure provides methods and systems for solving an optimization problem using a computing platform comprising at least one non-classical computer and at least one digital computer. The at least one non-classical computer may be configured to perform an adiabatic quantum computation with a first Hamiltonian and second Hamiltonian.

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: The present disclosure provides methods and systems for stochastic optimization of a robust inference problem using a sampling device.

Abstract: A method and a system are disclosed for solving a dynamic programming problem using a quantum computer. The method comprises receiving an indication of a dynamic programming problem, the dynamic programming problem comprising a plurality of transition kernels, receiving data representative of the dynamic programming problem, generating at least one oracle for the transition kernels of the dynamic programming problem, until a stopping criterion is met determining at least one linear programming problem for the dynamic programming problem, solving the at least one linear programming problem using a quantum computer comprising the generated at least one oracle to determine at least one solution, and providing the determined at least one solution; and providing a solution to the dynamic programming problem.

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 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.