Machine learning consists of three essential parts as data, model, and optimization. We review these in short and then consider several generalizations into their quantum versions, namely quantum machine learning. In optimization, we consider a generalization of the loss function with a noncommutable operator. The result demonstrates the superiority in generalization performance when we add this noncommutable operator. Next, we discuss quantum machine learning with the quantum model. The implementation of the quantum model is now realizable by various quantum devices appearing so far. How to use the quantum device and compute several necessary quantities are described.

Based on the general framework of the Kubo and Luttinger’s linear response theory, we clarified the range of validity of Boltzmann transport theory for thermoelectric response using a quite general model including both periodic and random potentials, electron-phonon interaction, and electron-electron interaction. As two typical examples beyond the Boltzmann transport regime, we introduce (i) the band-edge engineering of thermoelectric power factor of semi-conducting carbon nanotubes and (ii) the huge Seebeck coefficient of FeSb₂ due to the phonon drag associated with impurity band in the narrow band gap.

A minimal model of the jamming transition is a system consisting of spherical frictionless spherical particles. In this paper, we first review the numerical and theoretical results of this model in two and three dimensions. In particular, we discuss that the critical exponents do not depend on the spatial dimensions, implying that the upper critical dimension of the jamming transition is blow two dimensions. Next, we discuss our recent numerical results in a quasi-one-dimensional system. We show that the critical exponents in the quasi-one-dimensional system differ from those in two and three dimensions. Furthermore, the gap distribution remains finite even at the jamming transition point. Our work, for the first time, unveils the scaling behavior of the jamming transition below the upper critical dimension.

Spin current, a flow of the spin degree of freedom in condensed matter, is a fundamental concept in spintronics research. Many experimental and theoretical investigations are devoted to developing creation/annihilation and control methods of the spin current. Deep into microscopic views, the spin current in magnetic insulators is carried by the transverse component of spin-waves (quantized magnons). Magnons can be polarized, and the magnon polarization, i.e., the direction of the precessional motion of the electronic spin, affects the thermodynamics of magnetic materials, governing the magnitude and sign of the spin current. However, the magnon polarization of magnon modes has eluded experimental observation. We measure the mode-resolved magnon polarization of the quintessential magnet Y₃Fe₅O₁₂ (YIG), through the chiral term detection of inelastic polarized neutron scattering. There exist major two magnon modes, and the gap separating optical and acoustic modes is of the order of the thermal energy at room temperature. A maximum of the observed spin current near room temperature has been interpreted in terms of the competition between magnon modes with opposite polarization. Our experimental findings are well accounted for by atomistic spin dynamics calculations of the scattering cross section.

Group testing is an effective method in identifying infected patients in a population to reduce the number of tests and correct test errors. In group testing, tests are performed on pools of specimens collected from patients, where the number of pools is smaller than that of patients. The performance of group testing depends on the design of pools and algorithms that are used for inferring the infected patients from the test outcomes. We study an adaptive pooling method based on the predictive distribution in the framework of Bayesian inference. Using a belief propagation algorithm, the proposed method results in more accurate identification of the infected patients, compared with the group testing performed on randomly designed pools.