Satoshi Morita

Mathematical foundation of quantum annealing

Quantum annealing is a generic name of quantum algorithms that use quantum-mechanical fluctuations to search for the solution of an optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum computation. The present paper reviews the mathematical and theoretical foundations of quantum annealing. In particular, theorems are presented for convergence conditions of quantum annealing to the target optimal state after an infinite-time evolution following the Schrodinger or stochastic (Monte Carlo) dynamics. It is proved that the same asymptotic behavior of the control parameter guarantees convergence for both the Schrodinger dynamics and the stochastic dynamics in spite of the essential difference of these two types of dynamics. Also described are the prescriptions to reduce errors in the final approximate solution obtained after a long but finite dynamical evolution of quantum annealing. It is shown there that we can reduce errors significantly by an ingenious choice of annealing schedule (time dependence of the control parameter) without compromising computational complexity qualitatively. A review is given on the derivation of the convergence condition for classical simulated annealing from the view point of quantum adiabaticity using a classical-quantum mapping.

Estimation of forearm movement from EMG signal and application to prosthetic hand control

In this paper, a new approach is examined for controlling the prosthetic hand: the torque control of each joint. The joint torque is estimated from EMG signals using an artificial neural network. The learning system is based on a feedback error learning schema. Two controlled objects were used in the experiments, i.e. a hand dynamic model and prosthetic hand. These experimental results show the possibility to apply the proposed method to the prosthetic hand control under the conditions that the controlled object is a second order delay system.

Observations Of Flares And Active Regions From Yohkoh, and Magnetodynamic Models Explaining Them

We discuss here some of the new aspects about solar flares and active regions found by the Solar X-ray Satellite Yohkoh, by taking advantage of the wider dynamic range and higher cadence observations with higher spatial resolution compared with the previous satellites. Those new aspects have lead us to new ways of understandings, with contradictions to the previous views about flares and active regions that are widely conceived for a long time. We give some models that explain those newly revealed observational results.

Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections

The nature of quantum spin liquids is studied for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, J1, and those between next-nearest-neighbor sites, J2. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region 0.4 < J2/J1 ≤ 0.6 sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of 0.4 < J2/J1 ≤ 0.5, while the gapped valence-bond-crystal (VBC) phase is stabilized for 0.5 < J2/J1 ≤ 0.6. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the C4v symmetry. The power-law behaviors of the spin–spin and dimer–dimer correlation functions in the gapless reg...

Gapless Spin-Liquid Phase in an Extended Spin 1/2 Triangular Heisenberg Model

We numerically study Heisenberg models on modified triangular lattices, and show that a weak next-nearest-neighbor exchange interaction added to a simple triangular lattice, namely, the equilateral triangular lattice with only the nearest-neighbor exchange is sufficient to stabilize a quantum spin liquid against the antiferromagnetic order widely accepted as the ground state of the simple triangular model. The spin gap (triplet excitation gap) and spin correlation at long distances decay algebraically with increasing system size at the critical point between the antiferromagnetic and spin-liquid phases as well as inside the spin-liquid phase, indicating the presence of an unconventional critical (algebraic spin-liquid) phase characterized by the dynamical and anomalous critical exponents z+eta sim 1. Unusually small triplet and singlet excitation energies found in extended points of the Brillouin zone impose constraints on this algebraic spin liquid.

Griffiths inequalities for the Gaussian spin glass

The Griffiths inequalities for Ising spin-glass models with Gaussian randomness of non-vanishing mean are proved using properties of the Gaussian distribution and gauge symmetry of the system. These inequalities imply that correlation functions are non-negative and monotonic along the Nishimori line in the phase diagram. From this result, the existence of thermodynamic limit for correlation functions and pressure is proved under free and fixed boundary conditions. Relations between the location of multicritical points are also derived for different lattices.

Convergence theorems for quantum annealing

We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular, the property of strong ergodicity is proved for the path-integral Monte Carlo implementation of quantum annealing for the transverse Ising model under a power decay of the transverse field. This result is to be compared with the much slower inverse-log decay of temperature in the conventional simulated annealing. Similar results are proved for the Greens function Monte Carlo approach. Optimization problems in continuous space of particle configurations are also discussed.

Prosthetic hand control based on torque estimation from EMG signals

In this paper, we propose a direct torque control method for the prosthetic hand. In order to estimate the joint torque from EMG signals, an artificial neural network by the feedback error learning schema is used. 2-DOF motions, i.e. hand grasping/opening and arm flexion/extension, are picked up. In the experiments, two measurement conditions of EMG signal are prepared: the forearm from which the EMG signal is measured is free or fixed. Then it is verified that the neural network can learn the relation between the EMG signal and the joint torque under these two measurement conditions.

Convergence of Quantum Annealing with Real-Time Schrödinger Dynamics

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrodinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Greens function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et al. for the analysis of classical simulate...

Surface Terms on the Nishimori Line of the Gaussian Edwards-Anderson Model

For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure, i.e., the difference between the pressure of a box and the sum of the pressures of adjacent sub-boxes in which the box can been decomposed. We show that all those terms indeed behave proportionally to the surface size and prove the existence in the thermodynamic limit of the adjacency pressure.