Abstract: A computing device, including memory, an accelerator device, and a processor. The processor may generate a plurality of data packs that each indicate an update to a variable of one or more variables of a combinatorial cost function. The processor may transmit the plurality of data packs to the accelerator device. The accelerator device may, for each data pack, retrieve a variable value of the variable indicated by the data pack and generate an updated variable value. The accelerator device may generate an updated cost function value based on the updated variable value. The accelerator device may be further configured to determine a transition probability using a Monte Carlo algorithm and may store the updated variable value and the updated cost function value with the transition probability. The accelerator device may output a final updated cost function value to the processor.

Abstract: A computing system including one or more processing devices configured to generate a training data set. Generating the training data set may include generating training molecular structures, respective training Hamiltonians, and training energy terms. Computing the training energy terms may include, for each of the training Hamiltonians, computing a kinetic energy term, a nuclear potential energy term, an electron repulsion energy term, and an exchange energy term using Hartree-Fock (HF) estimation. Computing the training energy terms may further include, for a first subset of the training Hamiltonians, computing dynamical correlation energy terms using coupled cluster estimation. Computing the training energy terms may further include, for a second subset of the first subset, generating truncated Hamiltonians and computing static correlation energy terms using complete active space (CAS) estimation.

Abstract: A method of training a quantum computer employs quantum algorithms. The method comprises loading, into the quantum computer, a description of a quantum Boltzmann machine, and training the quantum Boltzmann machine according to a protocol, wherein a classification error is used as a metric for the protocol.

Abstract: A computing device is provided, including memory storing a cost function of a plurality of variables. The computing device may further include a processor configured to, for a stochastic simulation algorithm, compute a control parameter upper bound. The processor may compute a control parameter lower bound. The processor may compute a plurality of intermediate control parameter values within a control parameter range between the control parameter lower bound and the control parameter upper bound. The processor may compute an estimated minimum or an estimated maximum of the cost function using the stochastic simulation algorithm with the control parameter upper bound, the control parameter lower bound, and the plurality of intermediate control parameter values. A plurality of copies of the cost function may be simulated with a respective plurality of seed values.

Abstract: Example circuit implementations of Szegedy's quantization of the Metropolis-Hastings walk are presented. In certain disclosed embodiments, a quantum walk procedure of a Markov chain Monte Carlo simulation is implemented in which a quantum move register is reset at every step in the quantum walk. In further embodiments, a quantum walk procedure of a Markov chain Monte Carlo simulation is implemented in which an underlying classical walk is obtained using a Metropolis-Hastings rotation or a Glauber dynamics rotation. In some embodiments, a quantum walk procedure is performed in the quantum computing device to implement a Markov Chain Monte Carlo method; during the quantum walk procedure, an intermediate measurement is obtained; and a rewinding procedure of one or more but not all steps of the quantum walk procedure is performed if the intermediate measurement produces an incorrect outcome.

Abstract: A computing device, including memory, an accelerator device, and a processor. The processor may generate a plurality of data packs that each indicate an update to a variable of one or more variables of a combinatorial cost function. The processor may transmit the plurality of data packs to the accelerator device. The accelerator device may, for each data pack, retrieve a variable value of the variable indicated by the data pack and generate an updated variable value. The accelerator device may generate an updated cost function value based on the updated variable value. The accelerator device may be further configured to determine a transition probability using a Monte Carlo algorithm and may store the updated variable value and the updated cost function value with the transition probability. The accelerator device may output a final updated cost function value to the processor.

Abstract: A computing device is provided, including a cluster update accelerator circuit configured to receive signals encoding a combinatorial cost function of a plurality of variables and a connectivity graph for the combinatorial cost function. In an energy sum phase, the cluster update accelerator circuit may determine a respective plurality of accumulated energy change values for the combinatorial cost function based at least in part on the connectivity graph. In an update phase, the cluster update accelerator circuit may determine a respective update indicator bit for each accumulated energy change value. In an encoder phase, based on the plurality of update indicator bits, the cluster update accelerator circuit may select a largest update-indicated cluster of the variables included in the connectivity graph. The cluster update accelerator circuit may output an instruction to update the variables included in the largest update-indicated cluster.

Abstract: A computing device, including memory, an accelerator device, and a processor. The processor may generate a plurality of data packs that each indicate an update to a variable of one or more variables of a combinatorial cost function. The processor may transmit the plurality of data packs to the accelerator device. The accelerator device may, for each data pack, retrieve a variable value of the variable indicated by the data pack and generate an updated variable value. The accelerator device may generate an updated cost function value based on the updated variable value. The accelerator device may be further configured to determine a transition probability using a Monte Carlo algorithm and may store the updated variable value and the updated cost function value with the transition probability. The accelerator device may output a final updated cost function value to the processor.

Abstract: A computing device is provided, including memory storing a cost function of a plurality of variables. The computing device may further include a processor configured to, for a stochastic simulation algorithm, compute a control parameter upper bound. The processor may compute a control parameter lower bound. The processor may compute a plurality of intermediate control parameter values within a control parameter range between the control parameter lower bound and the control parameter upper bound. The processor may compute an estimated minimum or an estimated maximum of the cost function using the stochastic simulation algorithm with the control parameter upper bound, the control parameter lower bound, and the plurality of intermediate control parameter values. A plurality of copies of the cost function may be simulated with a respective plurality of seed values.

Abstract: A computing device is provided, including memory storing a cost function of a plurality of variables. The computing device may further include a processor configured to, for a stochastic simulation algorithm, compute a control parameter upper bound. The processor may compute a control parameter lower bound. The processor may compute a plurality of intermediate control parameter values within a control parameter range between the control parameter lower bound and the control parameter upper bound. The processor may compute an estimated minimum or an estimated maximum of the cost function using the stochastic simulation algorithm with the control parameter upper bound, the control parameter lower bound, and the plurality of intermediate control parameter values. A plurality of copies of the cost function may be simulated with a respective plurality of seed values.

Abstract: A computing device is provided, including a cluster update accelerator circuit configured to receive signals encoding a combinatorial cost function of a plurality of variables and a connectivity graph for the combinatorial cost function. In an energy sum phase, the cluster update accelerator circuit may determine a respective plurality of accumulated energy change values for the combinatorial cost function based at least in part on the connectivity graph. In an update phase, the cluster update accelerator circuit may determine a respective update indicator bit for each accumulated energy change value. In an encoder phase, based on the plurality of update indicator bits, the cluster update accelerator circuit may select a largest update-indicated cluster of the variables included in the connectivity graph. The cluster update accelerator circuit may output an instruction to update the variables included in the largest update-indicated cluster.

Abstract: A computing device is provided, including memory storing a cost function of a plurality of variables. The computing device may further include a processor configured to, for a stochastic simulation algorithm, compute a control parameter upper bound. The processor may compute a control parameter lower bound. The processor may compute a plurality of intermediate control parameter values within a control parameter range between the control parameter lower bound and the control parameter upper bound. The processor may compute an estimated minimum or an estimated maximum of the cost function using the stochastic simulation algorithm with the control parameter upper bound, the control parameter lower bound, and the plurality of intermediate control parameter values. A plurality of copies of the cost function may be simulated with a respective plurality of seed values.

Abstract: Embodiments of a new approach for training a class of quantum neural networks called quantum Boltzmann machines are disclosed. in particular examples, methods for supervised training of a quantum Boltzmann machine are disclosed using an ensemble of quantum states that the Boltzmann machine is trained to replicate. Unlike existing approaches to Boltzmann training, example embodiments as disclosed herein allow for supervised training even in cases where only quantum examples are known (and not probabilities from quantum measurements of a set of states). Further, this approach does not require the use of approximations such as the Golden-Thompson inequality.

Abstract: A computing device, including memory, an accelerator device, and a processor. The processor may generate a plurality of data packs that each indicate an update to a variable of one or more variables of a combinatorial cost function. The processor may transmit the plurality of data packs to the accelerator device. The accelerator device may, for each data pack, retrieve a variable value of the variable indicated by the data pack and generate an updated variable value. The accelerator device may generate an updated cost function value based on the updated variable value. The accelerator device may be further configured to determine a transition probability using a Monte Carlo algorithm and may store the updated variable value and the updated cost function value with the transition probability. The accelerator device may output a final updated cost function value to the processor.

Abstract: Example circuit implementations of Szegedy's quantization of the Metropolis-Hastings walk are presented. In certain disclosed embodiments, a quantum walk procedure of a Markov chain Monte Carlo simulation is implemented in which a quantum move register is reset at every step in the quantum walk. In further embodiments, a quantum walk procedure of a Markov chain Monte Carlo simulation is implemented in which an underlying classical walk is obtained using a Metropolis-Hastings rotation or a Glauber dynamics rotation. In some embodiments, a quantum walk procedure is performed in the quantum computing device to implement a Markov Chain Monte Carlo method; during the quantum walk procedure, an intermediate measurement is obtained; and a rewinding procedure of one or more but not all steps of the quantum walk procedure is performed if the intermediate measurement produces an incorrect outcome.

Abstract: In some examples, techniques and architectures for solving combinatorial optimization or statistical sampling problems use a recursive hierarchical approach that involves reinitializing various subsets of a set of variables. The entire set of variables may correspond to a first level of a hierarchy. In individual steps of the recursive process of solving an optimization problem, the set of variables may be partitioned into subsets corresponding to higher-order levels of the hierarchy, such as a second level, a third level, and so on. Variables of individual subsets may be randomly initialized. Based on the objective function, a combinatorial optimization operation may be performed on the individual subsets to modify variables of the individual subsets. Reinitializing subsets of variables instead of reinitializing the entire set of variables may allow for preservation of information gained in previous combinatorial optimization operations.

Abstract: Operators such as unitary operators common in quantum mechanical applications may be approximated by a Trotter-like approximation. An operator may be decomposed and terms of the operator may be grouped, or assigned into levels. The levels may be scaled and applied at unique intervals of calculational steps. A quantum device may have circuitry for applying levels of the operator at the unique intervals.

Abstract: In some examples, techniques and architectures for solving combinatorial optimization or statistical sampling problems use a hierarchical approach. Such a hierarchical approach may be applied to a system or process in a patch-like fashion. A set of elements of the system correspond to a first tier. An objective function associates the set of elements with one another. The set of elements are partitioned into patches corresponding to a second tier. The patches individually include second tier elements that are subsets of the set of elements, and the individual patches have an energy configuration. The second tier elements of the patches are randomly initialized. Based, at least in part, on the objective function, a combinatorial optimization operation is performed on the second tier elements of the individual patches to modify the second tier elements of the individual patches.

Abstract: A quantum annealer simulator approximates unitary quantum dynamics of a quantum annealer on a non-quantum computing device such as a conventional computing device. The quantum annealer simulator may utilize algorithms that may efficiently approximate unitary time evolution of a quantum system, where the quantum system corresponds to a problem for which an optimized solution is sought.

Abstract: Operators such as unitary operators common in quantum mechanical applications may be approximated by a Trotter-like approximation. An operator may be decomposed and terms of the operator may be grouped, or assigned into levels. The levels may be scaled and applied at unique intervals of calculational steps. A quantum device may have circuitry for applying levels of the operator at the unique intervals.