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Papers - TANAKA Shu

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Machine Learning Supported Annealing for Prediction of Grand Canonical Crystal Structures

Couzinié Y., Seki Y., Nishiya Y., Nishi H., Kosugi T., Tanaka S., Matsushita Y.I.

Journal of the Physical Society of Japan 94 ( 4 ) 2025.04

ISSN 00319015

This study investigates the application of Factorization Machines with Quantum Annealing (FMQA) to address the crystal structure problem (CSP) in materials science. FMQA is a black-box optimization algorithm that combines machine learning with annealing machines to find samples to a black-box function that minimize a given loss. The CSP involves determining the optimal arrangement of atoms in a material based on its chemical composition, a critical challenge in materials science. We explore FMQA’s ability to efficiently sample optimal crystal configurations by setting the loss function to the energy of the crystal configuration as given by a predefined interatomic potential. Further, we investigate how well the energies of the various metastable configurations, or local minima of the potential, are learned by the algorithm. Our investigation reveals FMQA’s potential in quick ground state sampling and in recovering relational order between local minima.

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Formulation of Correction Term in QUBO Form for Phase-Field Model

Aoki S., Endo K., Matsuda Y., Seki Y., Tanaka S., Muramatsu M.

International Journal for Numerical Methods in Engineering 126 ( 6 ) 2025.03

ISSN 00295981

In this study, we developed a method of estimating the correction terms that makes the Hamiltonian used in phase-field analysis by quantum annealing correspond to the free energy functional of the conventional phase-field analysis using the finite difference method. For the estimation of the correction terms, we employed a factorization machine. The inputs to the factorization machine were the phase-field variables in domain-wall encoding and the differences between the Gibbs free energy and Hamiltonian. We obtained the difference value in quadratic unconstrained binary optimization (QUBO) form as the output of learning using the factorization machine. The QUBO form difference was subjected to the original Hamiltonian as the correction term. The performance of this correction term was evaluated by calculating the energy for a equilibrium state of diblock copolymer. In phase-field analysis, the time evolution equation is formulated so that the total free energy decreases; hence, a lower the free energy means a more accurate result close to that of a conventional method. When we performed annealing with correction terms, the microstructure showed a Gibbs free energy that was lower than that obtained without the correction terms.

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Advantages of Fixing Spins in Quantum Annealing

Hattori T., Irie H., Kadowaki T., Tanaka S.

Journal of the Physical Society of Japan 94 ( 1 ) 2025.01

ISSN 00319015

Quantum annealing can efficiently obtain solutions to combinatorial optimization problems. Size-reduction methods are used to treat large-scale combinatorial optimization problems that cannot be input directly into a quantum annealer because of its size limitation. Various size-reduction methods using fixing spins have been proposed as quantum-classical hybrid methods to obtain solutions. However, the high performance of these hybrid methods is yet to be clearly elucidated. In this study, we adopted a parameterized fixing spins method to verify the effects of fixing spins. The results revealed that setting the appropriate number of spins of the subproblem is crucial for obtaining a satisfactory solution, and the energy gap expansion is confirmed after fixing spins.

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Inductive Construction of Variational Quantum Circuit for Constrained Combinatorial Optimization

Nakada H., Tanahashi K., Tanaka S.

IEEE Access 13 73096 - 73108 2025

In this study, we propose a new method for constrained combinatorial optimization using variational quantum circuits. Quantum computers are considered to have the potential to solve large combinatorial optimization problems faster than classical computers. Variational quantum algorithms, such as Variational Quantum Eigensolver (VQE), have been studied extensively because they are expected to work on noisy intermediate scale devices. Unfortunately, many optimization problems have constraints, which induces infeasible solutions during VQE process. Recently, several methods for efficiently solving constrained combinatorial optimization problems have been proposed by designing a quantum circuit so as to output only the states that satisfy the constraints. However, the types of available constraints are still limited. Therefore, we have started to develop variational quantum circuits that can handle a wider range of constraints. The proposed method utilizes a forwarding operation that maps from feasible states for subproblems to those for larger subproblems. As long as appropriate forwarding operations can be defined, iteration of this process can inductively construct variational circuits outputting feasible states even in the case of multiple and complex constraints. In this paper, the proposed method was applied to facility location problem. As a result, feasible solutions were obtained with 100%, and the probability of obtaining optimal solutions was over 22 times higher than that of conventional VQEs. Nevertheless, the cost of the obtained circuit was comparable to that of conventional circuits.

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Development of optimization method for truss structure by quantum annealing

Honda R., Endo K., Kaji T., Suzuki Y., Matsuda Y., Tanaka S., Muramatsu M.

Scientific Reports 14 ( 1 ) 2024.12

In this study, we developed a new method of topology optimization for truss structures by quantum annealing. To perform quantum annealing analysis with real variables, representation of real numbers as a sum of random number combinations is employed. The nodal displacement is expressed with binary variables. The Hamiltonian H is formulated on the basis of the elastic strain energy and position energy of a truss structure. It is confirmed that truss deformation analysis is possible by quantum annealing. For the analysis of the optimization method for the truss structure, the cross-sectional area of the truss is expressed with binary variables. The iterative calculation for the changes in displacement and cross-sectional area leads to the optimal structure under the prescribed boundary conditions.

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Novel real number representations in Ising machines and performance evaluation: Combinatorial random number sum and constant division

Endo K., Matsuda Y., Tanaka S., Muramatsu M.

PLoS ONE 19 ( 6 June ) 2024.06

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Static and Dynamic Analysis of Energy Landscape Transformation of the Ising Problems

Kanai H., Tanaka S.

Proceedings - IEEE Quantum Week 2024, QCE 2024 2 374 - 375 2024

Ising machines are promising next-generation computers that aim to efficiently obtain good solutions to combinatorial optimization problems, which are converted to the Ising model. To obtain the ground state of the Ising model with high accuracy, tuning the hyperparameters in the Ising model is of great importance. Recently, a new method called Energy Landscape Transformation of Ising Problems (ELTIP) has been proposed which does not change any of the original eigenenergies at all. The previous study demonstrated that the Time-to-Solution (TTS) of Quantum Annealing (QA) decreases for the specific problems after ELTIP. We reveal the scope of the problems where ELTIP can be sufficiently beneficial. To this end, we analyze the correlation between the mean Hamming distance and the ground state probability in both the static and dynamic analysis.

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Physical Properties of Error Reduction Algorithms for Ising Machines

Hino K., Tanaka S.

Proceedings - IEEE Quantum Week 2024, QCE 2024 2 434 - 435 2024

Ising machines are expected to be dedicated computers that are capable of efficiently searching for good solutions to combinatorial optimization problems. When solving combinatorial optimization problems with an Ising machine, the objective function and constraints of the combinatorial optimization problems are expressed using the Ising model. Then, the low-energy states of the Ising model are searched by the internal algorithms of Ising machines. Typical internal algorithms are Simulated Annealing (SA) and Quantum Annealing (QA). Both algorithms exhibit stochastic behavior, so the final solution may contain errors. Therefore, it is an essential issue in the field of Ising machines to reduce errors as much as possible. A previous study proposed an error reduction method for QA machines, namely the Quantum Annealing Correction (QAC) model. This method reduces error by introducing penalty interaction and performing a specific decoding method. Building on these valuable insights, we proposed an alternative error reduction method, the stacked model. To verify the effectiveness, we examined on the relationship between the penalty interaction and the success probability of the QAC model and the stacked model on SA. The obtained results differ from the facts observed in QA. In summary, a decoding method different from the one considered effective in QA was found to be effective in SA. This result suggests that when considering an appropriate error reduction method, it is necessary to consider the internal algorithm of the Ising machine.

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Annealing-Assisted Column Generation for Inequality-Constrained Combinatorial Optimization Problems

Kanai H., Yamashita M., Tanahashi K., Tanaka S.

IEEE Access 12 157669 - 157685 2024

Ising machines are expected to solve combinatorial optimization problems faster than the existing integer programming solvers. These problems, particularly those encountered in practical situations, typically involve inequality constraints. However, owing to the hardware limitations of the current Ising machines, solving combinatorial optimization problems with inequality constraints remains challenging. The Capacitated Vehicle Routing Problem (CVRP) is a typical example of a problem with inequality constraints. The CVRP is classified as NP-hard and, thus, is commonly solved using heuristic algorithms, such as column generation. Column generation attempts to iteratively generate only the promising routes, as the number of feasible routes increases exponentially. Within this framework, the CVRP is formulated as a set cover problem. The corresponding dual solutions are used to define the pricing subproblem, which is intended to create a new route. By applying Ising machines to this pricing subproblem, the overall computation time can be reduced. This study aims to solve combinatorial optimization problems with inequality constraints using a hybrid algorithm that combines column generation and Ising machines, thereby extending the applications of the latter. Additionally, we introduced limited column generation, wherein we fixed the decision variables to eliminate the overlap between the generated columns. By reducing unnecessary variables, our proposed method can overcome the hardware limitations where a small number of variables is available on real devices. We parameterize the difficulty of the inequality constraints and demonstrate that our annealing-assisted column generation can converge to a better lower bound.