Nonnegative/Binary matrix factorization for image classification using quantum annealing.

Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute. Demonstrating the benefits of this integration now becomes essential. With the advance of quantum computing, several machine-learning techniques have been proposed that use quantum annealing. In this study, we implement a matrix factorization method using quantum annealing for image classification and compare the performance with traditional machine-learning methods. Nonnegative/binary matrix factorization (NBMF) was originally introduced as a generative model, and we propose a multiclass classification model as an application. We extract the features of handwritten digit images using NBMF and apply them to solve the classification problem. Our findings show that when the amount of data, features, and epochs is small, the accuracy of models trained by NBMF is superior to classical machine-learning methods, such as neural networks. Moreover, we found that training models using a quantum annealing solver significantly reduces computation time. Under certain conditions, there is a benefit to using quantum annealing technology with machine learning.

Correction: Kudo, K. Localization Detection Based on Quantum Dynamics. Entropy 2022, 24, 1085.

In the original publication [...].

Localization Detection Based on Quantum Dynamics.

Detecting many-body localization (MBL) typically requires the calculation of high-energy eigenstates using numerical approaches. This study investigates methods that assume the use of a quantum device to detect disorder-induced localization. Numerical simulations for small systems demonstrate how the magnetization and twist overlap, which can be easily obtained from the measurement of qubits in a quantum device, changing from the thermal phase to the localized phase. The twist overlap evaluated using the wave function at the end of the time evolution behaves similarly to the one evaluated with eigenstates in the middle of the energy spectrum under a specific condition. The twist overlap evaluated using the wave function after time evolution for many disorder realizations is a promising probe for detecting MBL in quantum computing approaches.

Distance-based clustering using QUBO formulations.

In computer science, clustering is a technique for grouping data. Ising machines can solve distance-based clustering problems described by quadratic unconstrained binary optimization (QUBO) formulations. A typical simple method using an Ising machine makes each cluster size equal and is not suitable for clustering unevenly distributed data. We propose a new clustering method that provides better performance than the simple method, especially for unevenly distributed data. The proposed method is a hybrid algorithm including an iterative process that comprises solving a discrete optimization problem with an Ising machine and calculating parameters with a general-purpose computer. To minimize the communication overhead between the Ising machine and the general-purpose computer, we employed a low-latency Ising machine implementing the simulated bifurcation algorithm with a field-programmable gate array attached to a local server. The proposed method results in clustering 200 unevenly distributed data points with a clustering score 18% higher than that of the simple method. The discrete optimization with 2000 variables is performed 100 times per iteration, and the overhead time is reduced to approximately 20% of the total execution time. These results suggest that hybrid algorithms using Ising machines can efficiently solve practical optimization problems.

Sol-Gel Coexisting Phase of Polymer Microgels Triggers Spontaneous Buckling.

Mechanical buckling is a ubiquitous phenomenon of elastic bodies like core-shell microgels. Although conventional theory predicts that sufficiently high pressure is the primary factor inducing the buckling of core-shell microgels, they often buckle spontaneously without applying pressure. We explored such spontaneous buckling of microgels by introducing interfacial tension between the gel phase of the shell and sol phase of the core. Thus, we found that the core-shell microgels in a sol-gel coexisting phase with a certain shell thickness ratio exhibit spontaneous buckling. According to our theoretical analysis, spontaneous buckling occurs due to the balance between the gel elasticity E and interfacial tension γ when the characteristic length γ/ E is comparable to the microgel size R. Moreover, we found that the ratio between γ/ E and R determines the buckling condition of the shell thickness ratio. Our findings establish an important framework for applying spontaneous buckling to the shape control of elastic bodies.

Emergence of Wrinkles during the Curing of Coatings.

Wrinkles often emerge on a paint layer when a second coat of paint is applied on an already-coated substrate. Wrinkle formation occurs when the first layer absorbs organic solvent from the second layer. We set up experiments to mimic the double-coating process, focusing on the interaction between a paint layer and an organic solvent. In the experiments, we investigated the characteristic wavelengths of the wrinkles and the time of wrinkle emergence. We employed a simple model to explain the wrinkle emergence and performed numerical simulations. The linear stability analysis of the model provides a relation between the wavelengths and the characteristic timescale that agrees reasonably well with our experimental data as well as numerical results. Our results indicate that compression of the layer due to swelling and delamination are both important factors in the formation of wrinkles.

Assessing potential countermeasures against the dengue epidemic in non-tropical urban cities.

BACKGROUND: Dengue is a common mosquito-borne viral disease epidemic especially in tropical and sub-tropical regions where water sanitation is not substantially controlled. However, dengue epidemics sometimes occur in non-tropical urban cities with substantial water sanitary control. Using a mathematical model, we investigate what conditions can be important for a dengue epidemic to occur in an urban city such as Tokyo, where vectors are active only in summer and there are little number of vectors around hosts. METHODS: The model, which is a modified Ross-Macdonald model, consists of two sets of host-vector compartments. The two sets correspond to high-risk and low-risk areas, and only hosts can move between them. Assuming that mosquitoes have constant activity for only 90 days, we assess five potential countermeasures: (1) restricted movement between the two areas, (2) insecticide application, (3) use of repellents, (4) vector control, and (5) isolation of the infected. RESULTS: The basic reproduction number R 0 and the cumulative number of infected hosts for 90 days are evaluated for each of the five countermeasures. In the cases of Measures 2-5, the cumulative number of the infected for 90 days can be reduced substantially for small R 0 even if R 0>1. Although R 0 for Measure 1 monotonically decreases with the mobility rates, the cumulative number of the infected for 90 days has a maximum at a moderate mobility rate. If the mobility rate is sufficiently small, the restricted movement effectively increases the number density of vectors in the high-risk area, and the epidemic starts earlier in the high-risk area than in the low-risk one, while the growth of infections is slow. CONCLUSIONS: Measures 2-5 are more or less effective. However, Measure 1 can have the opposite effect, depending on the mobility rates. The restricted movement results in the formation of a kind of core population, which can promote the epidemic in the entire population.

Effects of Landau-Lifshitz-Gilbert damping on domain growth.

Domain patterns are simulated by the Landau-Lifshitz-Gilbert (LLG) equation with an easy-axis anisotropy. If the Gilbert damping is removed from the LLG equation, it merely describes the precession of magnetization with a ferromagnetic interaction. However, even without the damping, domains that look similar to those of scalar fields are formed, and they grow with time. It is demonstrated that the damping has no significant effects on domain growth laws and large-scale domain structure. In contrast, small-scale domain structure is affected by the damping. The difference in small-scale structure arises from energy dissipation due to the damping.

Magnetic domain patterns on strong perpendicular magnetization of Co/Ni multilayers as spintronics materials: I. Dynamic observations.

Materials with perpendicular magnetic anisotropy can reduce the threshold current density of the current-induced domain wall motion. Co/Ni multilayers show strong perpendicular magnetic anisotropy and therefore it has become a highly potential candidate of current-induced domain wall motion memories. However, the details of the mechanism which stabilizes the strong perpendicular magnetization in Co/Ni multilayers have not yet been understood. In the present work, the evolution of the magnetic domain structure of multilayers consisting of pairs of 2 or 3 monolayers (ML) of Ni and 1 ML of Co on W(110) was investigated during growth with spin-polarized low-energy electron microscopy. An interesting phenomenon, that the magnetic domain structure changed drastically during growth, was revealed. In the early stages of the growth the magnetization alternated between in-plane upon Co deposition and out-of-plane upon Ni deposition. The change of the magnetization direction occurred within a range of less than 0.2 ML during Ni or Co deposition, with break-up of the existing domains followed by growth of new domains. The Ni and Co thickness at which the magnetization direction switched shifted gradually with the number of Co/Ni pairs. Above 3-4 Co/Ni pairs it stayed out-of-plane. The results indicate clearly that the Co-Ni interfaces play the important role of enhancing the perpendicular magnetic anisotropy.

Magnetic domain patterns on strong perpendicular magnetization of Co/Ni multilayers as spintronics materials: II. Numerical simulations.

Magnetic domains in ultrathin films form domain patterns, which strongly depend on the magnetic anisotropy. The magnetic anisotropy in Co/Ni multilayers changes with the number of layers. We provide a model to simulate the experimentally observed domain patterns. The model assumes a layer-dependent magnetic anisotropy. With the anisotropy parameter estimated from experimental data, we reproduce the magnetic domain patterns.

Level statistics of a pseudo-Hermitian Dicke model.

A non-Hermitian operator that is related to its adjoint through a similarity transformation is defined as a pseudo-Hermitian operator. We study the level statistics of a pseudo-Hermitian Dicke Hamiltonian that undergoes quantum phase transition (QPT). We find that the level-spacing distribution of this Hamiltonian near the integrable limit is close to Poisson distribution, while it is Wigner distribution for the ranges of the parameters for which the Hamiltonian is nonintegrable. We show that the assertion in the context of the standard Dicke model that QPT is a precursor to a change in the level statistics is not valid in general.

Effects of an oscillating field on magnetic domain patterns: Emergence of concentric-ring patterns surrounding a strong defect.

Oscillating fields can make domain patterns change into various types of structures. Numerical simulations show that concentric-ring domain patterns centered at a strong defect are observed under a rapidly oscillating field in some cases. The concentric-ring pattern appears near the threshold of spatially uniform patterns in high-frequency cases. The threshold is theoretically estimated and the theoretical threshold is in good agreement with numerical one in a high-frequency region. The theoretical analysis gives also good estimations of several characteristics of domain patterns for high frequencies.

Effects of an oscillating field on pattern formation in a ferromagnetic thin film: analysis of patterns traveling at a low velocity.

Magnetic domain patterns under an oscillating field are studied theoretically by using a simple Ising-like model. We propose two ways to investigate the effects of the oscillating field. The first one leads to a model in which rapidly oscillating terms are averaged out and the model can explain the existence of the maximum amplitude of the field for the appearance of patterns. The second one leads to a model that includes the delay of the response to the field and the model suggests the existence of a traveling pattern which moves very slowly compared with the time scale of the driving field.