Application of QUBO solver using black-box optimization to structural design for resonance avoidance.

Quadratic unconstrained binary optimization (QUBO) solvers can be applied to design an optimal structure to avoid resonance. QUBO algorithms that work on a classical or quantum device have succeeded in some industrial applications. However, their applications are still limited due to the difficulty of transforming from the original optimization problem to QUBO. Recently, black-box optimization (BBO) methods have been proposed to tackle this issue using a machine learning technique and a Bayesian treatment for combinatorial optimization. We propose a BBO method based on factorization machine to design a printed circuit board for resonance avoidance. This design problem is formulated to maximize natural frequency and simultaneously minimize the number of mounting points. The natural frequency, which is the bottleneck for the QUBO formulation, is approximated to a quadratic model in the BBO method. For the efficient approximation around the optimum solution, in the proposed method, we probabilistically generate the neighbors of the optimized solution of the current model and update the model. We demonstrated that the proposed method can find the optimum mounting point positions in shorter calculation time and higher success probability of finding the optimal solution than a conventional BBO method. Our results can open up QUBO solvers' potential for other applications in structural designs.

Visualizing Invisible Phase Transitions in Blue Phase Liquid Crystals Using Early Warning Indicators.

Changes in the statistical properties of data as a system approaches a critical transition is studied intensively as early warning signals, but their application to materials science, where phase transitions-a type of critical transition-are of fundamental importance, are limited. Here, a critical transition analysis is applied to time-series data from a microscopic 3D ordered soft material-blue phase liquid crystals (BPLC)-and demonstrates that phase transitions that are invisible under ambient conditions can be visualized through the choice of appropriate early warning indicators. After discussing how a phase transition affects the statistical properties in a system with a Landau-de Gennes type free energy potential, the predicted changes are experimentally observed at the two types of phase transitions that occur in a BPLC: the isotropic to simple cubic, and simple cubic to body-centered cubic transitions. In particular, it is shown that the skewness of the intensity distribution inverts its sign at the phase transition, enabling temporally and spatially resolved mapping of phase transitions. This approach can be easily adapted to a wide variety of material systems and microscopy techniques, providing a powerful tool for studying complex critical transition phenomena.

Traffic signal optimization on a square lattice with quantum annealing.

The spread of intelligent transportation systems in urban cities has caused heavy computational loads, requiring a novel architecture for managing large-scale traffic. In this study, we develop a method for globally controlling traffic signals arranged on a square lattice by means of a quantum annealing machine, namely the D-Wave quantum annealer. We first formulate a signal optimization problem that minimizes the imbalance of traffic flows in two orthogonal directions. Then we reformulate this problem as an Ising Hamiltonian, which is compatible with quantum annealers. The new control method is compared with a conventional local control method for a large 50-by-50 city, and the results exhibit the superiority of our global control method in suppressing traffic imbalance over wide parameter ranges. Furthermore, the solutions to the global control method obtained with the quantum annealing machine are better than those obtained with conventional simulated annealing. In addition, we prove analytically that the local and the global control methods converge at the limit where cars have equal probabilities for turning and going straight. These results are verified with numerical experiments.

Early-warning signals using dynamical network markers selected by covariance.

It is an important issue, particularly in the context of sustainable society, to predict critical transitions across which a system state abruptly shifts toward a contrasting state. In this study, we propose an indicator of critical transitions in multivariate dynamical systems, based on the concept of the dynamical network marker (DNM). The DNM is originally defined based on the eigendecomposition of the Jacobian matrix of a nonlinear system and corresponds to large-magnitude components of the dominant eigenvector, which contributes primarily to transitions. Our DNM-based indicator is derived from the sample covariance matrix of state variables in a target system. Simulation results to predict transitions in complex network systems consisting of a harvesting model consistently show the superiority of our indicator as a precursor of transitions regardless of network structure characteristics, as compared to a conventional indicator.