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In the present study, we demonstrate how to perform, using quantum annealing, the singular value decomposition and the principal component analysis. Quantum annealing gives a way to find a ground state of a system, while the singular value decomposition requires the maximum eigenstate. The key idea is to transform the sign of the final Hamiltonian, and the maximum eigenstate is obtained by quantum annealing. Furthermore, the adiabatic time scale is obtained by the approximation focusing on the maximum eigenvalue., Comment: 6 pages, 4 figures

In the present study, we propose a new perspective on thermal dissipation based on the thermo field dynamics. From the view point of the renormalization theory, there appear effective interactions between the original and tilde spaces on thermo field dynamics with reducing thermal disturbances. This study yields the equivalence of the following two pictures, namely such a spin system with a random field due to a heat bath as is defined in a Hilbert space and a finite-size system with effective interactions defined in a double Hilbert space. The correspondence of the above two systems yields such perspective that the thermal disturbance is described by the effective non-Hermitian interactions., Comment: 12pages 2figures

In the present study, we focus on the parity of the order parameters and clarify the order formation process in a system including two order parameters. Each order parameter shows each different parity under a gauge transformation, namely even and odd order parameters. For example, in a spin-glass model, the even order parameter corresponds to the spin-glass order parameter while the odd one corresponds to the magnetization. We introduce phenomenologically a set of Langevin equations to express the ordering process under a white Gaussian noise. Using two kinds of Fokker-Planck equations, we analyze the order formation process and the entropy production. Furthermore, we show the noise dependence of the onset time., Comment: 19 pages, 5 figures