Abstract: A processing system includes a processor configured to perform an annealing process to individually control, depending on time, each contribution of a cost function, a transverse field function, and an orthogonal field function, and perform an optimization process to sequentially determine an optimal value of the contribution of the orthogonal field function based on a final state of the annealing process. The processor is configured to extract the qubit that optimizes an evaluation indicator for the final state of the annealing process in which an intensity parameter for maximizing the orthogonal field function is varied, based on a gradient caused by the variation. The processor is configured to determine the intensity parameter that gives the optimal value for the extracted qubit based on the gradient, and output an optimal solution of the combinatorial optimization problem by mapping a set of the intensity parameters determined for each of the qubits.

Abstract: An arithmetic apparatus includes a control unit that changes a first weighting coefficient assigned to a constraint term included in Hamiltonian so that the first weighting coefficient changes differently from a second weighting coefficient assigned to an objective term included in the Hamiltonian in process of reducing quantum fluctuations to obtain a ground state of the Hamiltonian used for solving a combinatorial optimization problem.

Abstract: The efficiency of quantum annealing on an LHZ model is improved. An arithmetic apparatus includes an arithmetic unit configured to adjust an intensity schedule function in quantum annealing of a constraint term expressed by many-body interactions in an LHZ model by a hybrid algorithm that uses a value of the intensity schedule function at one time point or each of a plurality of time points as a variational parameter.