Embedding Quantum-Inspired Technology into Material Research Tools: A Strategy for Invisibility and Productivity

In this study, we develop a framework for formulating different types of problems in materials science as QUBO instances by designing Hamiltonians tailored to the structure of each problem.As an example of physical simulation, we represent the time evolution of a particle system as an energy minimization problem. The energy function is constructed from terms corresponding to mass conservation, particle interactions, and stabilization of specific states. By minimizing this energy, the sequential state transitions of the system can be expressed within a QUBO formulation.As a second case, we consider a data analysis problem in which dependencies among features are modeled as a directed acyclic graph (DAG). Since the dependency matrix obtained from observed data does not generally satisfy the DAG constraint, we introduce a permutation matrix representing the ordering of features and optimize it such that the dependency matrix becomes strictly upper triangular. As the permutation matrix is composed of binary variables, the sum of squared lower-triangular elements can be defined as a Hamiltonian, enabling the formulation of DAG construction as a QUBO problem.Through these formulations, both physical processes and structure learning problems can be treated in a unified manner as optimization problems suitable for quantum annealing.

To validate the proposed approach, numerical experiments were conducted using a simulated quantum annealer. For the physical simulation case, a diffusion process was considered, where the spatial spread of particles over time was formulated as a QUBO problem. The implementation involved approximately 8,000 binary variables, and the time evolution was reproduced through energy minimization. The obtained results were compared with theoretical models, confirming quantitative agreement in their temporal behavior.For the DAG construction problem, experiments were conducted using a public dataset (load_diabetes). Feature dependencies were estimated, and a DAG structure was constructed by optimizing the permutation matrix. In this formulation, the number of binary variables scales as d^2 for d features; nevertheless, stable structural patterns were successfully extracted from real data.Furthermore, to facilitate practical usage, the data analysis algorithm was implemented as an application in which the underlying QUBO formulation and optimization processes are embedded and hidden from the user interface. This design allows users to perform dependency structure analysis without requiring knowledge of quantum computing or optimization details.

Quantum annealing does not guarantee convergence to the global optimum; however, it can provide high-quality approximate solutions within practical time scales. This characteristic is particularly advantageous for problems where stochastic behavior and solution diversity are important.The diffusion simulation considered in this study is one such example, as real physical systems exhibit stochastic dynamics due to thermal fluctuations. In this context, the ability to naturally capture non-deterministic transitions, rather than strictly following energy minima, makes the approach suitable for approximate simulation of such systems.Similarly, in DAG estimation, real-world data often contain noise, making it difficult to uniquely determine fine-grained structures. By performing multiple optimization runs and extracting consistent patterns across solutions, it is possible to identify reliable global structures.On the other hand, the proposed approach faces challenges in scalability, as the number of QUBO variables increases with problem size. In particular, for DAG construction, the number of variables scales as O(d^2), requiring strategies such as problem decomposition and hybridization with classical computation for large-scale applications.From an implementation perspective, embedding quantum-related optimization techniques into application-level tools-such that the underlying computational mechanisms remain largely invisible to users-enables their use by researchers without specialized expertise. Such an implementation strategy provides a practical pathway for introducing quantum-inspired optimization methods into materials research workflows.