Hidetoshi Nishimori

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We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the quality of restoration/decoding is maximized at a specific set of parameter values determined by the source and channel(More)
We study the performance of quantum annealing for systems with ground-state degeneracy by directly solving the Schrödinger equation for small systems and quantum Monte Carlo simulations for larger systems. The results indicate that naive quantum annealing using a transverse field may not be well suited to identify all degenerate ground-state configurations,(More)
The gauge theory of spin glasses and statistical-mechanical formulation of errorcorrecting codes are reviewed with an emphasis on their similarities. For the gauge theory, we explain the functional identities on dynamical autocorrelation functions and on the distribution functions of order parameters. These functional identities restrict the possibilities(More)
The microscopic probability distribution function of the Sherrington-Kirkpatrick (SK) model of spin glasses is calculated explicitly as a function of time by a hightemperature expansion. The resulting formula to the third order of the inverse temperature shows that an assumption made by Coolen, Laughton and Sherrington in their recent theory of dynamics is(More)
The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in neural network research, we utilize a perceptron of which the transfer function is appropriately designed in order to compress and decode the(More)
We prove weak ergodicity of the inhomogeneous Markov process generated by the generalized transition probability of Tsallis and Stariolo under power-law decay of the temperature. We thus have a mathematical foundation to conjecture convergence of simulated annealing processes with the generalized transition probability to the minimum of the cost function.(More)
We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true(More)