Abstract: A user interface (UI), data structures and algorithms facilitate programming, analyzing, debugging, embedding, and/or modifying problems that are embedded or to be embedded on an analog processor (e.g., quantum processor), increasing computational efficiency and/or accuracy of problem solutions. The UI provides graph representations (e.g., source graph, target graph and correspondence therebetween) with nodes and edges which may map to hardware components (e.g., qubits, couplers) of the analog processor. Characteristics of solutions are advantageously represented spatially associated (e.g., overlaid or nested) with characteristics of a problem. Characteristics (e.g., bias state) may be represented by color, pattern, values, icons. Issues (e.g., broken chains) may be detected and alerts provided.

Abstract: Systems and methods are described for operating a hybrid computing system using cluster contraction for converting large, dense input to reduced input that can be easily mapped into a quantum processor. The reduced input represents the global structure of the problem. Techniques involve partitioning the input variables into clusters and contracting each cluster. The input variables can be partitioned using an Unweighted Pair Group Method with Arithmetic Mean algorithm. The quantum processor returns samples based on the reduced input and the samples are expanded to correspond to the original input.

Abstract: Hybrid quantum-classical approaches for solving computational problems in which results from a quantum processor are combined with an exact method executed on a classical processor are described. Quantum processors can generate candidate solutions to a combinatorial optimization problem, but since quantum processors can be probabilistic, they are unable to certify that a solution is an optimal solution. A hybrid quantum-classical exact solver addresses this problem by combining outputs from a quantum annealing processor with a classical exact algorithm that is modified to exploit properties of the quantum computation. The exact method executed on a classical processor can be a Branch and Bound algorithm. A Branch and Bound algorithm can be modified to exploit properties of quantum computation including a) the sampling of multiple low-energy solutions by a quantum processor, and b) the embedding of solutions in a regular structure such as a native hardware graph of a quantum processor.

Abstract: A user interface (UI), data structures and algorithms facilitate programming, analyzing, debugging, embedding, and/or modifying problems that are embedded or to be embedded on an analog processor (e.g., quantum processor), increasing computational efficiency and/or accuracy of problem solutions. The UI provides graph representations (e.g., source graph, target graph and correspondence therebetween) with nodes and edges which may map to hardware components (e.g., qubits, couplers) of the analog processor. Characteristics of solutions are advantageously represented spatially associated (e.g., overlaid or nested) with characteristics of a problem. Characteristics (e.g., bias state) may be represented by color, pattern, values, icons. Issues (e.g., broken chains) may be detected and alerts provided.

Abstract: Systems and methods are described for operating a hybrid computing system using cluster contraction for converting large, dense input to reduced input that can be easily mapped into a quantum processor. The reduced input represents the global structure of the problem. Techniques involve partitioning the input variables into clusters and contracting each cluster. The input variables can be partitioned using an Unweighted Pair Group Method with Arithmetic Mean algorithm. The quantum processor returns samples based on the reduced input and the samples are expanded to correspond to the original input.

Abstract: A hybrid computing system for solving a computational problem includes a digital processor, a quantum processor having qubits and coupling devices that together define a working graph of the quantum processor, and at least one nontransitory processor-readable medium communicatively coupleable to the digital processor which stores at least one of processor-executable instructions or data. The digital processor receives a computational problem, and programs the quantum processor with a first set of bias fields and a first set of coupling strengths. The quantum processor generates samples as potential solutions to an approximation of the problem. The digital processor updates the approximation by determining a second set of bias fields based at least in part on the first set of bias fields and a first set of mean fields that are based at least in part on the first set of samples and coupling strengths of one or more virtual coupling devices.

Abstract: Methods for solving discrete quadratic models are described. The methods compute an energy of each state of each variable based on its interaction with other variables, exponential weights, and normalized probabilities proportional to the exponential weights. The energy of each variable is computed as a function of the magnitude of each variable and a current state of all other variables, exponential weights, the feasible region for each variable, and normalized probabilities, proportional to the exponential weights and respecting constraints. Methods executed via a hybrid computing system obtain two candidate values for each variable; constructs a Hamiltonian that uses a binary value to determine which candidate values each variable should take, then constructs a binary quadratic model based on the Hamiltonian. Samples from the binary quadratic model are obtained via a quantum processor.

Abstract: A highly parallelized parallel tempering technique for simulating dynamic systems, such as quantum processors, is provided. Replica exchange is facilitated by synchronizing grid-level memory. Particular implementations for simulating quantum processors by representing cells of qubits and couplers in grid-, block-, and thread-level memory are discussed. Parallel tempering of such dynamic systems can be assisted by modifying replicas based on isoenergetic cluster moves (ICMs). ICMs are generated via secondary replicas which are maintained alongside primary replicas and exchanged between blocks and/or generated dynamically by blocks without necessarily being exchanged. Certain refinements, such as exchanging energies and temperatures through grid-level memory, are also discussed.

Abstract: Systems and methods are described for operating a hybrid computing system using cluster contraction for converting large, dense input to reduced input that can be easily mapped into a quantum processor. The reduced input represents the global structure of the problem. Techniques involve partitioning the input variables into clusters and contracting each cluster. The input variables can be partitioned using an Unweighted Pair Group Method with Arithmetic Mean algorithm. The quantum processor returns samples based on the reduced input and the samples are expanded to correspond to the original input.

Abstract: A user interface (UI), data structures and algorithms facilitate programming, analyzing, debugging, embedding, and/or modifying problems that are embedded or to be embedded on an analog processor (e.g., quantum processor), increasing computational efficiency and/or accuracy of problem solutions. The UI provides graph representations (e.g., source graph, target graph and correspondence therebetween) with nodes and edges which may map to hardware components (e.g., qubits, couplers) of the analog processor. Characteristics of solutions are advantageously represented spatially associated (e.g., overlaid or nested) with characteristics of a problem. Characteristics (e.g., bias state) may be represented by color, pattern, values, icons. Issues (e.g., broken chains) may be detected and alerts provided.

Abstract: A user interface (UI), data structures and algorithms facilitate programming, analyzing, debugging, embedding, and/or modifying problems that are embedded or to be embedded on an analog processor (e.g., quantum processor), increasing computational efficiency and/or accuracy of problem solutions. The UI provides graph representations (e.g., source graph, target graph and correspondence therebetween) with nodes and edges which may map to hardware components (e.g., qubits, couplers) of the analog processor. Characteristics of solutions are advantageously represented spatially associated (e.g., overlaid or nested) with characteristics of a problem. Characteristics (e.g., bias state) may be represented by color, pattern, values, icons. Issues (e.g., broken chains) may be detected and alerts provided.

Abstract: A user interface (UI), data structures and algorithms facilitate programming, analyzing, debugging, embedding, and/or modifying problems that are embedded or to be embedded on an analog processor (e.g., quantum processor), increasing computational efficiency and/or accuracy of problem solutions. The UI provides graph representations (e.g., source graph, target graph and correspondence therebetween) with nodes and edges which may map to hardware components (e.g., qubits, couplers) of the analog processor. Characteristics of solutions are advantageously represented spatially associated (e.g., overlaid or nested) with characteristics of a problem. Characteristics (e.g., bias state) may be represented by color, pattern, values, icons. Issues (e.g., broken chains) may be detected and alerts provided.

Abstract: A hybrid computing system for solving a computational problem includes a digital processor, a quantum processor having qubits and coupling devices that together define a working graph of the quantum processor, and at least one nontransitory processor-readable medium communicatively coupleable to the digital processor which stores at least one of processor-executable instructions or data. The digital processor receives a computational problem, and programs the quantum processor with a first set of bias fields and a first set of coupling strengths. The quantum processor generates samples as potential solutions to an approximation of the problem. The digital processor updates the approximation by determining a second set of bias fields based at least in part on the first set of bias fields and a first set of mean fields that are based at least in part on the first set of samples and coupling strengths of one or more virtual coupling devices.

Abstract: A highly parallelized parallel tempering technique for simulating dynamic systems, such as quantum processors, is provided. Replica exchange is facilitated by synchronizing grid-level memory. Particular implementations for simulating quantum processors by representing cells of qubits and couplers in grid-, block-, and thread-level memory are discussed. Parallel tempering of such dynamic systems can be assisted by modifying replicas based on isoenergetic cluster moves (ICMs). ICMs are generated via secondary replicas which are maintained alongside primary replicas and exchanged between blocks and/or generated dynamically by blocks without necessarily being exchanged. Certain refinements, such as exchanging energies and temperatures through grid-level memory, are also discussed.

Abstract: Hybrid quantum-classical approaches for solving computational problems in which results from a quantum processor are combined with an exact method executed on a classical processor are described. Quantum processors can generate candidate solutions to a combinatorial optimization problem, but since quantum processors can be probabilistic, they are unable to certify that a solution is an optimal solution. A hybrid quantum-classical exact solver addresses this problem by combining outputs from a quantum annealing processor with a classical exact algorithm that is modified to exploit properties of the quantum computation. The exact method executed on a classical processor can be a Branch and Bound algorithm. A Branch and Bound algorithm can be modified to exploit properties of quantum computation including a) the sampling of multiple low-energy solutions by a quantum processor, and b) the embedding of solutions in a regular structure such as a native hardware graph of a quantum processor.

Abstract: Systems and methods are described for operating a hybrid computing system using cluster contraction for converting large, dense input to reduced input that can be easily mapped into a quantum processor. The reduced input represents the global structure of the problem. Techniques involve partitioning the input variables into clusters and contracting each cluster. The input variables can be partitioned using an Unweighted Pair Group Method with Arithmetic Mean algorithm. The quantum processor returns samples based on the reduced input and the samples are expanded to correspond to the original input.