Quickly obtaining optimal solutions of combinatorial optimization problems has tremendous value but is extremely difficult. Thus, various kinds of machines specially designed for combinatorial optimization have recently been proposed and developed. Toward the realization of higher-performance machines, here, we propose an algorithm based on classical mechanics, which is obtained by modifying a previously proposed algorithm called simulated bifurcation. Our proposed algorithm allows us to achieve not only high speed by parallel computing but also high solution accuracy for problems with up to one million binary variables. Benchmarking shows that our machine based on the algorithm achieves high performance compared to recently developed machines, including a quantum annealer using a superconducting circuit, a coherent Ising machine using a laser, and digital processors based on various algorithms. Thus, high-performance combinatorial optimization is realized by massively parallel implementations of the proposed algorithm based on classical mechanics.

An effective model that describes the Kondo effect due to a point defect in graphene is developed, taking account of the electronic state and the lattice structure of the defect. It is shown that this model can be transformed into a singlechannel pseudogap Anderson model with a finite chemical potential. On the basis of the numerical renormalization group method, it is clarified that the experimentally observed gate-voltage dependence of the Kondo temperature is understood in this framework.

We numerically study reservoir computing on a spin-torque oscillator (STO) array, describing magnetization dynamics of the STO array by a nonlinear oscillator model. The STOs exhibit synchronized oscillation due to coupling by magnetic dipolar fields. We show that the reservoir computing can be performed by using the synchronized oscillation state. Its performance can be improved by increasing the number of the STOs. The performance becomes the highest at the boundary between the synchronized and disordered states. Using the STO array, we can achieve higher performance than an echo-state network with similar number of units. This result indicates that the STO array is promising for hardware implementation of reservoir computing.

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A two-dimensional array of Kerr-nonlinear parametric oscillators (KPOs) with local four-body interactions is a promising candidate for realizing an Ising machine with all-to-all spin couplings, based on adiabatic quantum computation in the Lechner–Hauke–Zoller (LHZ) scheme. However, its performance has been evaluated only for a symmetric network of three KPOs, and thus it has been unclear whether such an Ising machine works in general cases with asymmetric networks. By numerically simulating an asymmetric network of more KPOs in the LHZ scheme, we find that the asymmetry in the four-body interactions causes inhomogeneity in photon numbers and hence degrades the performance. We then propose a method for reducing the inhomogeneity, where the discrepancies of the photon numbers are corrected by tuning the detunings of KPOs depending on their positions, without monitoring their states during adiabatic time evolution. Our simulation results show that the performance can be dramatically improved by this method. The proposed method, which is based on the understanding of the asymmetry, is expected to be useful for general networks of KPOs in the LHZ scheme and thus for their large-scale implementation.

Quantum annealing, which is particularly useful for combinatorial optimization, becomes more powerful by using excited states, in addition to ground states. However, such excited-state quantum annealing is prone to errors due to dissipation. Here we propose excited-state quantum annealing started with the most stable state, i.e., vacuum states. This counterintuitive approach becomes possible by using effective energy eigenstates of driven quantum systems. To demonstrate this concept, we use a network of Kerr-nonlinear parametric oscillators, where we can start excited-state quantum annealing with the vacuum state of the network by appropriately setting initial detuning frequencies for the oscillators. By numerical simulations of four oscillators, we show that the present approach can solve some hard instances whose optimal solutions cannot be obtained by standard ground-state quantum annealing because of energy-gap closing. In this approach, a nonadiabatic transition at an energy-gap closing point is rather utilized. We also show that this approach is robust against errors due to dissipation, as expected, compared to quantum annealing started with physical excited (i.e., nonvacuum) states. These results open new possibilities for quantum computation and driven quantum systems.

Layer-selective manipulation of magnetization direction in a multilayer magnetic structure offers a way to develop a large-capacity magnetic recording device with multiple recording layers. Here, we use a double-layer perpendicular magnetic nanodot consisting of two layers with low and high perpendicular magnetic anisotropy (PMA) and show that layer-selective magnetization switching can be accomplished by utilizing a microwave-assisted magnetization switching technique. Since the low-and high-PMA magnetic layers have different ferromagnetic resonance (FMR) frequencies, their magnetization excitation that reduces the switching field can be individually induced by adjusting the frequency of the applied microwave field (rf), and this principle allows rf to select the layer to be switched. In addition, by measuring thermally excited FMR signals from the nanodot, we find that the magnetization dynamics of the two PMA layers couple through interactions, and we identify the excitation modes responsible for the layer-selective magnetization switching.

To meet the ever-increasing demand for data storage, future magnetic recording devices will need to be made three-dimensional by implementing multilayer recording. In this article, we present methods of detecting and manipulating the magnetization direction of a specific layer selectively in a vertically stacked multilayer magnetic system, which enable layer-selective read and write operations in three-dimensional magnetic recording devices. The principle behind the methods is ferromagnetic resonance excitation in a microwave magnetic field. By designing each magnetic recording layer to have a different ferromagnetic resonance frequency, magnetization excitation can be induced individually in each layer by tuning the frequency of an applied microwave magnetic field, and this selective magnetization excitation can be utilized for the layer-selective operations. Regarding media for three-dimensional recording, when layers of a perpendicular magnetic material are vertically stacked, dipolar interaction between multiple recording layers arises and is expected to cause problems, such as degradation of thermal stability and switching field distribution. To solve these problems, we propose the use of an antiferromagnetically coupled structure consisting of hard and soft magnetic layers. Because the stray fields from these two layers cancel each other, antiferromagnetically coupled media can reduce the dipolar interaction.