Design of Magnetic Lattices with a Quantum-Inspired Evolutionary Optimization Algorithm

This article investigates the identification of magnetic spin distributions in ferromagnetic materials by minimizing the system's free energy. Magnetic lattices of varying sizes are constructed, and the free energy is computed using an Ising model that accounts for spin-to-spin neighbor interactions and the influence of an external magnetic field. The problem reduces to determining the state of each spin, either up or down, leading to an optimization problem with $2^{n \times n}$ design variables for an $n \times n$ lattice. To address the high-dimensional and computationally intractable nature of this problem, particularly for large domains, we employ a quantum optimization algorithm, BQP. The BQP results are first validated against solutions obtained using a genetic algorithm for smaller lattices. Finally, the approach is extended to large-scale systems, including $50 \times 50$ lattices, where conventional methods become impractical.