Abstract: Computational systems implement problem solving using hybrid digital/quantum computing approaches. A problem may be represented as a problem graph which is larger and/or has higher connectivity than a working and/or hardware graph of a quantum processor. A quantum processor may be used determine approximate solutions, which solutions are provided as initial states to one or more digital processors which may implement classical post-processing to generate improved solutions. Techniques for solving problems on extended, more-connected, and/or “virtual full yield” variations of the processor's actual working and/or hardware graphs are provided. A method of operation in a computational system comprising a quantum processor includes partitioning a problem graph into sub-problem graphs, and embedding a sub-problem graph onto the working graph of the quantum processor. The quantum processor and a non-quantum processor-based device generate partial samples.

Abstract: Computational systems implement problem solving using hybrid digital/quantum computing approaches. A problem may be represented as a problem graph which is larger and/or has higher connectivity than a working and/or hardware graph of a quantum processor. A quantum processor may be used determine approximate solutions, which solutions are provided as initial states to one or more digital processors which may implement classical post-processing to generate improved solutions. Techniques for solving problems on extended, more-connected, and/or “virtual full yield” variations of the processor's actual working and/or hardware graphs are provided. A method of operation in a computational system comprising a quantum processor includes partitioning a problem graph into sub-problem graphs, and embedding a sub-problem graph onto the working graph of the quantum processor. The quantum processor and a non-quantum processor-based device generate partial samples.

Abstract: Computational systems implement problem solving using hybrid digital/quantum computing approaches. A problem may be represented as a problem graph which is larger and/or has higher connectivity than a working and/or hardware graph of a quantum processor. A quantum processor may be used determine approximate solutions, which solutions are provided as initial states to one or more digital processors which may implement classical post-processing to generate improved solutions. Techniques for solving problems on extended, more-connected, and/or “virtual full yield” variations of the processor's actual working and/or hardware graphs are provided. A method of operation in a computational system comprising a quantum processor includes partitioning a problem graph into sub-problem graphs, and embedding a sub-problem graph onto the working graph of the quantum processor. The quantum processor and a non-quantum processor-based device generate partial samples.

Abstract: A hybrid computing system comprising a quantum computer and a digital computer employs a digital computer to use machine learning methods for post-processing samples drawn from the quantum computer. Post-processing samples can include simulating samples drawn from the quantum computer. Machine learning methods such as generative adversarial networks (GANs) and conditional GANs are applied. Samples drawn from the quantum computer can be a target distribution. A generator of a GAN generates samples based on a noise prior distribution and a discriminator of a GAN measures the distance between the target distribution and a generative distribution. A generator parameter and a discriminator parameter are respectively minimized and maximized.

Abstract: Computational systems implement problem solving using hybrid digital/quantum computing approaches. A problem may be represented as a problem graph which is larger and/or has higher connectivity than a working and/or hardware graph of a quantum processor. A quantum processor may be used determine approximate solutions, which solutions are provided as initial states to one or more digital processors which may implement classical post-processing to generate improved solutions. Techniques for solving problems on extended, more-connected, and/or “virtual full yield” variations of the processor's actual working and/or hardware graphs are provided. A method of operation in a computational system comprising a quantum processor includes partitioning a problem graph into sub-problem graphs, and embedding a sub-problem graph onto the working graph of the quantum processor. The quantum processor and a non-quantum processor-based device generate partial samples.

Abstract: A computational system can include digital circuitry and analog circuitry, for instance a digital processor and a quantum processor. The quantum processor can operate as a sample generator providing samples. Samples can be employed by the digital processing in implementing various machine learning techniques. For example, the computational system can perform unsupervised learning over an input space, for example via a discrete variational auto-encoder, and attempting to maximize the log-likelihood of an observed dataset. Maximizing the log-likelihood of the observed dataset can include generating a hierarchical approximating posterior. Unsupervised learning can include generating samples of a prior distribution using the quantum processor. Generating samples using the quantum processor can include forming chains of qubits and representing discrete variables by chains.

Abstract: A computational system can include digital circuitry and analog circuitry, for instance a digital processor and a quantum processor. The quantum processor can operate as a sample generator providing samples. Samples can be employed by the digital processing in implementing various machine learning techniques. For example, the computational system can perform unsupervised learning over an input space, for example via a discrete variational auto-encoder, and attempting to maximize the log-likelihood of an observed dataset. Maximizing the log-likelihood of the observed dataset can include generating a hierarchical approximating posterior. Unsupervised learning can include generating samples of a prior distribution using the quantum processor. Generating samples using the quantum processor can include forming chains of qubits and representing discrete variables by chains.

Abstract: A hybrid computer comprising a quantum processor can be operated to perform a scalable comparison of high-entropy samplers. Performing a scalable comparison of high-entropy samplers can include comparing entropy and KL divergence of post-processed samplers. A hybrid computer comprising a quantum processor generates samples for machine learning. The quantum processor is trained by matching data statistics to statistics of the quantum processor. The quantum processor is tuned to match moments of the data.

Abstract: A hybrid computer comprising a quantum processor can be operated to perform a scalable comparison of high-entropy samplers. Performing a scalable comparison of high-entropy samplers can include comparing entropy and KL divergence of post-processed samplers. A hybrid computer comprising a quantum processor generates samples for machine learning. The quantum processor is trained by matching data statistics to statistics of the quantum processor. The quantum processor is tuned to match moments of the data.

Abstract: A hybrid computing system comprising a quantum computer and a digital computer employs a digital computer to use machine learning methods for post-processing samples drawn from the quantum computer. Post-processing samples can include simulating samples drawn from the quantum computer. Machine learning methods such as generative adversarial networks (GANs) and conditional GANs are applied. Samples drawn from the quantum computer can be a target distribution. A generator of a GAN generates samples based on a noise prior distribution and a discriminator of a GAN measures the distance between the target distribution and a generative distribution. A generator parameter and a discriminator parameter are respectively minimized and maximized.

Abstract: Computational systems implement problem solving using hybrid digital/quantum computing approaches. A problem may be represented as a problem graph which is larger and/or has higher connectivity than a working and/or hardware graph of a quantum processor. A quantum processor may be used determine approximate solutions, which solutions are provided as initial states to one or more digital processors which may implement classical post-processing to generate improved solutions. Techniques for solving problems on extended, more-connected, and/or “virtual full yield” variations of the processor's actual working and/or hardware graphs are provided. A method of operation in a computational system comprising a quantum processor includes partitioning a problem graph into sub-problem graphs, and embedding a sub-problem graph onto the working graph of the quantum processor. The quantum processor and a non-quantum processor-based device generate partial samples.

Abstract: Computational systems implement problem solving using hybrid digital/quantum computing approaches. A problem may be represented as a problem graph which is larger and/or has higher connectivity than a working and/or hardware graph of a quantum processor. A quantum processor may be used determine approximate solutions, which solutions are provided as initial states to one or more digital processors which may implement classical post-processing to generate improved solutions. Techniques for solving problems on extended, more-connected, and/or “virtual full yield” variations of the processor's actual working and/or hardware graphs are provided. A method of operation in a computational system comprising a quantum processor includes partitioning a problem graph into sub-problem graphs, and embedding a sub-problem graph onto the working graph of the quantum processor. The quantum processor and a non-quantum processor-based device generate partial samples.

Abstract: Methods and systems represent constraint as an Ising model penalty function and a penalty gap associated therewith, the penalty gap separating a set of feasible solutions to the constraint from a set of infeasible solutions to the constraint; and determines the Ising model penalty function subject to the bounds on the programmable parameters imposed by the hardware limitations of the second processor, where the penalty gap exceeds a predetermined threshold greater than zero. Such may be employed to find quantum binary optimization problems and associated gap values employing a variety of techniques.

Abstract: A computational system can include digital circuitry and analog circuitry, for instance a digital processor and a quantum processor. The quantum processor can operate as a sample generator providing samples. Samples can be employed by the digital processing in implementing various machine learning techniques. For example, the computational system can perform unsupervised learning over an input space, for example via a discrete variational auto-encoder, and attempting to maximize the log-likelihood of an observed dataset. Maximizing the log-likelihood of the observed dataset can include generating a hierarchical approximating posterior. Unsupervised learning can include generating samples of a prior distribution using the quantum processor. Generating samples using the quantum processor can include forming chains of qubits and representing discrete variables by chains.

Abstract: Computational systems implement problem solving using hybrid digital/quantum computing approaches. A problem may be represented as a problem graph which is larger and/or has higher connectivity than a working and/or hardware graph of a quantum processor. A quantum processor may be used determine approximate solutions, which solutions are provided as initial states to one or more digital processors which may implement classical post-processing to generate improved solutions. Techniques for solving problems on extended, more-connected, and/or “virtual full yield” variations of the processor's actual working and/or hardware graphs are provided. A method of operation in a computational system comprising a quantum processor includes partitioning a problem graph into sub-problem graphs, and embedding a sub-problem graph onto the working graph of the quantum processor. The quantum processor and a non-quantum processor-based device generate partial samples.

Abstract: A hybrid computer comprising a quantum processor can be operated to perform a scalable comparison of high-entropy samplers. Performing a scalable comparison of high-entropy samplers can include comparing entropy and KL divergence of post-processed samplers. A hybrid computer comprising a quantum processor generates samples for machine learning. The quantum processor is trained by matching data statistics to statistics of the quantum processor. The quantum processor is tuned to match moments of the data.

Abstract: Methods and systems represent constraint as an Ising model penalty function and a penalty gap associated therewith, the penalty gap separating a set of feasible solutions to the constraint from a set of infeasible solutions to the constraint; and determines the Ising model penalty function subject to the bounds on the programmable parameters imposed by the hardware limitations of the second processor, where the penalty gap exceeds a predetermined threshold greater than zero. Such may be employed to find quantum binary optimization problems and associated gap values employing a variety of techniques.

Abstract: A telecommunications mesh network includes a plurality of nodes each interconnected by an edge. A traffic demand is received having a working path with a link of edges interconnecting a source node with a destination node. The telecommunications mesh network has one or more pre-cross-connected trails associated therewith that are subdivided into one or more subtrails. Subtrails that do not meet pre-determined conditions are discarded. A logical graph representation of the telecommunications mesh network is created from subtrails that have not been discarded. Unused, shortcut, and rival edges are inserted into the logical graph. A shortest admissible protection path from the source node to the destination node is identified from the logical graph.