Ising machines are hardware that is expected to perform combinatorial optimization problems with high speed and high accuracy. In recent years, in the field of Ising machines, various studies have been conducted in each layer of hardware development, software development, and application search by both the academic side and industrial side. This manuscript explains how to use the Ising machine and introduces the current state of research and development in the field of Ising machines.

We will review the principles and applications of recently developing quantum annealers represented by D-Wave machines, and discuss the applicability to material materials science.

Quantum annealing is a method for finding the global minimum of a given objective function by using quantum fluctuations and is used mainly for combinatorial optimization problems where the search space is discrete. For ideal quantum annealing quantum bits which have long coherence time and scalability are necessary, and superconducting circuits are promising candidates for them. This is because high coherence is expected due to superconducting phenomena and high integration is realized by solid-state devices. In this paper quantum annealing based on superconducting parametric oscillators and related technology are introduced.

Digital Annealer developed by Fujitsu is a new architecture to solve “combinatorial optimization problems” at high speed with digital circuit inspired by quantum phenomena. The features are stable operation with digital circuit at room temperature, easy miniaturization, and easy mapping more complex problems with a fully-connected architecture. The Digital Annealer is easy to apply actual problems and contributes to customers in a wide range of businesses, including drug discovery, chemistry, manufacturing, transportation, finance, and logistics. In this article, we explain the fundamental of the Digital Annealer including the speedup technique. We also introduce an application to the material development using the Digital Annealer. The Digital Annealer is used to evaluate the structural similarity of the flavor molecules. We found that the molecules with high structural similarity show a similar flavor. We also extracted the common substructure of molecules having the similar flavor, which is considered to be the key structure of the flavor.

A new computing architecture, an annealing machine, which is specialized to solve combinatorial optimization problems, is proposed. The annealing machine maps combinatorial optimization problems to an Ising model and solves the problems by its own convergence property. We proposed a CMOS annealing machine, which is a CMOS implementation of the annealing machines. The CMOS annealing machine has an in-memory computing architecture for a high scalability. We constructed prototypes of the CMOS annealing machine. The 1st generation prototype with ASIC implementation, the 2nd generation prototype with FPGA implementation and the card-size prototype with 2-chip ASIC implementation are used to confirm its ability to solve combinatorial optimization problems and its high energy efficiency. The 2nd and card-size prototypes also confirm its multiple-chip operation, which enables a higher scalability of the CMOS annealing machine solving larger size optimization problems.

Recently, we have proposed a new heuristic algorithm for combinatorial optimization inspired by our proposed quantum computer. We named the algorithm “simulated bifurcation (SB) algorithm,” because it is based on the numerical simulation of nonlinear Hamiltonian systems exhibiting bifurcations. Here we present the principle, performance, and applications of our SB machine.

We worked on the development of technology for evaluating trace amounts of water-soluble impurities using Ion Chromatography(IC). The conditions were determined by grasping the measurement environment and the eluted ions from the equipment used for evaluation. For the sampling tool, we selected wipes and swabs with less eluting ions to reduce the effect on measured values and decided the evaluation procedure. It was found that analysis at the ppb level is possible by verifying IC measurement variability and detection limit. After grasping the background of the sampling tool, an L-shaped sample was manufactured and its cleanliness was evaluated. It was found that the amount of ions in the sample was larger than the background, and the difference was largely depending on the shape of the evaluation part. Therefore, we were able to establish a cleanliness evaluation method for vacuum equipment using IC.