Abstract: Systems and methods formulate problems for solving by a quantum processor using hardware graph decomposition. A decomposition of a primal graph may be built in a first stage based on a hardware specific graph, and refined in a second stage by, for example, removing vertices from the decomposition. The hardware specific graph may be a graph that is specific to a piece of hardware, for instance a quantum processor comprising a plurality of qubits and couplers operable to communicatively couple pairs of qubits.

Abstract: Solving computational problems may include generating a logic circuit representation of the computational problem, encoding the logic circuit representation as a discrete optimization problem, and solving the discrete optimization problem using a quantum processor. Output(s) of the logic circuit representation may be clamped such that the solving involves effectively executing the logic circuit representation in reverse to determine input(s) that corresponds to the clamped output(s). The representation may be of a Boolean logic circuit. The discrete optimization problem may be composed of a set of miniature optimization problems, where each miniature optimization problem encodes a respective logic gate from the logic circuit representation. A quantum processor may include multiple sets of qubits, each set coupled to respective annealing signal lines such that dynamic evolution of each set of qubits is controlled independently from the dynamic evolutions of the other sets of qubits.

Abstract: Solving computational problems may include generating a logic circuit representation of the computational problem, encoding the logic circuit representation as a discrete optimization problem, and solving the discrete optimization problem using a quantum processor. Output(s) of the logic circuit representation may be clamped such that the solving involves effectively executing the logic circuit representation in reverse to determine input(s) that corresponds to the clamped output(s). The representation may be of a multiplication circuit. The discrete optimization problem may be composed of a set of miniature optimization problems, where each miniature optimization problem encodes a respective logic gate from the logic circuit representation. A multiplication circuit may employ binary representations of factors, and these binary representations may be decomposed to reduce the total number of variables required to represent the multiplication circuit.

Abstract: Systems and methods formulate problems for solving by a quantum processor using hardware graph decomposition. A decomposition of a primal graph may be built in a first stage based on a hardware specific graph, and refined in a second stage by, for example, removing vertices from the decomposition. The hardware specific graph may be a graph that is specific to a piece of hardware, for instance a quantum processor comprising a plurality of qubits and couplers operable to communicatively couple pairs of qubits.

Abstract: Systems, devices, and methods for using an analog processor to solve computational problems. A digital processor is configured to track computational problem processing requests received from a plurality of different users, and to track at least one of a status and a processing cost for each of the computational problem processing requests. An analog processor, for example a quantum processor, is operable to assist in producing one or more solutions to computational problems identified by the computational problem processing requests via a physical evolution.

Abstract: Solving computational problems may include generating a logic circuit representation of the computational problem, encoding the logic circuit representation as a discrete optimization problem, and solving the discrete optimization problem using a quantum processor. Output(s) of the logic circuit representation may be clamped such that the solving involves effectively executing the logic circuit representation in reverse to determine input(s) that corresponds to the clamped output(s). The representation may be of a Boolean logic circuit. The discrete optimization problem may be composed of a set of miniature optimization problems, where each miniature optimization problem encodes a respective logic gate from the logic circuit representation. A quantum processor may include multiple sets of qubits, each set coupled to respective annealing signal lines such that dynamic evolution of each set of qubits is controlled independently from the dynamic evolutions of the other sets of qubits.

Abstract: Solving computational problems may include generating a logic circuit representation of the computational problem, encoding the logic circuit representation as a discrete optimization problem, and solving the discrete optimization problem using a quantum processor. Output(s) of the logic circuit representation may be clamped such that the solving involves effectively executing the logic circuit representation in reverse to determine input(s) that corresponds to the clamped output(s). The representation may be of a Boolean logic circuit. The discrete optimization problem may be composed of a set of miniature optimization problems, where each miniature optimization problem encodes a respective logic gate from the logic circuit representation. A quantum processor may include multiple sets of qubits, each set coupled to respective annealing signal lines such that dynamic evolution of each set of qubits is controlled independently from the dynamic evolutions of the other sets of qubits.

Abstract: Systems, devices, and methods for using an analog processor to solve computational problems. A digital processor is configured to track computational problem processing requests received from a plurality of different users, and to track at least one of a status and a processing cost for each of the computational problem processing requests. An analog processor, for example a quantum processor, is operable to assist in producing one or more solutions to computational problems identified by the computational problem processing requests via a physical evolution.

Abstract: An analog processor, for example a quantum processor may include a plurality of elongated qubits that are disposed with respect to one another such that each qubit may selectively be directly coupled to each of the other qubits via a single coupling device. Such may provide a fully interconnected topology.

Abstract: Systems, devices, and methods for using an analog processor to solve computational problems. A digital processor is configured to track computational problem processing requests received from a plurality of different users, and to track at least one of a status and a processing cost for each of the computational problem processing requests. An analog processor, for example a quantum processor, is operable to assist in producing one or more solutions to computational problems identified by the computational problem processing requests via a physical evolution.

Abstract: Solving computational problems may include generating a logic circuit representation of the computational problem, encoding the logic circuit representation as a discrete optimization problem, and solving the discrete optimization problem using a quantum processor. Output(s) of the logic circuit representation may be clamped such that the solving involves effectively executing the logic circuit representation in reverse to determine input(s) that corresponds to the clamped output(s). The representation may be of a Boolean logic circuit. The discrete optimization problem may be composed of a set of miniature optimization problems, where each miniature optimization problem encodes a respective logic gate from the logic circuit representation. A quantum processor may include multiple sets of qubits, each set coupled to respective annealing signal lines such that dynamic evolution of each set of qubits is controlled independently from the dynamic evolutions of the other sets of qubits.

Abstract: Discrete optimization problem are solved using an analog optimization device such as a quantum processor. Problems are solved using an objective function and at least one constraint corresponding to the discrete optimization problems. The objective function is converted into a first set of inputs and the at least one constraint is converted into a second set of inputs for the analog optimization device. A third set of inputs is generated which are indicative of at least one penalty coefficient. A final state of the analog optimization device corresponds to at least a portion of the solution to the discrete optimization problem.

Abstract: Systems, methods and articles solve computationally complex problems. Example embodiments provide data query language features that may be used to express optimization problems. An expression of an optimization problem in the provided data query language may be transformed into a primitive problem that is equivalent to the optimization problem. An optimization solver may be invoked to provide a solution to the primitive problem. Analog processors such as quantum processors as well as digital processors may be used to solve the primitive problem. This abstract is provided to comply with rules requiring an abstract, and is submitted with the intention that it will not be used to interpret or limit the scope or meaning of the claims.

Abstract: Systems, methods and articles for performing preference filtering on a database query. Example embodiments provide a new algorithm, called BNL#, that operates with a worst-case running time of O(ntce+ne+np) where {ne, np}<<nt?O(ntce). This represents an improvement over existing algorithms that are known in the art, such as the BNL algorithm which operates with a worst-case running time of O(nt2) and the BNL++ algorithm which operates with a worst-case running time of O(ntceneme), with ne<<nt. This abstract is provided to comply with rules requiring an abstract, and is submitted with the intention that it will not be used to interpret or limit the scope or meaning of the claims.

Abstract: An analog processor, for example a quantum processor may include a plurality of elongated qubits that are disposed with respect to one another such that each qubit may selectively be directly coupled to each of the other qubits via a single coupling device. Such may provide a fully interconnected topology.

Abstract: Systems, devices, and methods for using an analog processor to solve computational problems. A digital processor is configured to track computational problem processing requests received from a plurality of different users, and to track at least one of a status and a processing cost for each of the computational problem processing requests. An analog processor, for example a quantum processor, is operable to assist in producing one or more solutions to computational problems identified by the computational problem processing requests via a physical evolution.

Abstract: Discrete optimization problem are solved using an analog optimization device such as a quantum processor. Problems are solved using an objective function and at least one constraint corresponding to the discrete optimization problems. The objective function is converted into a first set of inputs and the at least one constraint is converted into a second set of inputs for the analog optimization device. A third set of inputs is generated which are indicative of at least one penalty coefficient. A final state of the analog optimization device corresponds to at least a portion of the solution to the discrete optimization problem.

Abstract: Analog processors such as quantum processors are employed to predict the native structures of proteins based on a primary structure of a protein. A target graph may be created of sufficient size to permit embedding of all possible native multi-dimensional topologies of the protein. At least one location in a target graph may be assigned to represent a respective amino acid forming the protein. An energy function is generated based assigned locations in the target graph. The energy function is mapped onto an analog processor, which is evolved from an initial state to a final state, the final state predicting a native structure of the protein.

Abstract: Systems, methods and apparatus for factoring numbers are provided. The factoring may be accomplished by creating a factor graph, mapping the factor graph onto an analog processor, initializing the analog processor to an initial state, evolving the analog processor to a final state, and receiving an output from the analog processor, the output comprising a set of factors of the number.

Abstract: The present invention presents a comprehensive system and method for operations management which has the reliability and adaptability to handle failures and changes respectively within the economic environment. The present invention presents a framework of features which include technology graphs, landscape representations and automated markets to achieve the requisite reliability and adaptability.