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.

High-performance combinatorial optimization based on classical mechanics.

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.

Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems.

Combinatorial optimization problems are ubiquitous but difficult to solve. Hardware devices for these problems have recently been developed by various approaches, including quantum computers. Inspired by recently proposed quantum adiabatic optimization using a nonlinear oscillator network, we propose a new optimization algorithm simulating adiabatic evolutions of classical nonlinear Hamiltonian systems exhibiting bifurcation phenomena, which we call simulated bifurcation (SB). SB is based on adiabatic and chaotic (ergodic) evolutions of nonlinear Hamiltonian systems. SB is also suitable for parallel computing because of its simultaneous updating. Implementing SB with a field-programmable gate array, we demonstrate that the SB machine can obtain good approximate solutions of an all-to-all connected 2000-node MAX-CUT problem in 0.5 ms, which is about 10 times faster than a state-of-the-art laser-based machine called a coherent Ising machine. SB will accelerate large-scale combinatorial optimization harnessing digital computer technologies and also offer a new application of computational and mathematical physics.

New linear-parabolic rate equation for thermal oxidation of silicon.

We propose a new oxidation rate equation for silicon supposing only a diffusion of oxidizing species but not including any rate-limiting step by interfacial reaction. It is supposed that diffusivity is suppressed in a strained oxide region near SiO(2)/Si the interface. The expression of a parabolic constant in the new equation is the same as that of the Deal-Grove model, while a linear constant makes a clear distinction with that of the model. The estimated thickness using the new expression is close to 1 nm, which compares well with the thickness of the structural transition layers.