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 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)
The gauge theory of spin glasses and statistical-mechanical formulation of error-correcting 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)
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 locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry, and the replica method. We find that the conjecture does not give the exact answer but leads to locations slightly(More)
The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice. Five different ordered phases, namely, ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase diagram. The spin-glass phase is more extensive when randomness is introduced within the planes than when it is(More)
We introduce antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term. We apply this method to the infinite-range ferromagnetic p-spin model, for which the conventional quantum annealing has been shown to have difficulties in finding the ground state efficiently due to a first-order transition. We(More)