Generating Hamiltonians with Known Minimum Energy Based on Ground-State Spin Logic for Probabilistic-Bit-Based Simulated Annealing
Naoya Onizawa, Takahiro Hanyu · 2025
A probabilistic bit (p-bit), considered a key element of probabilistic computing, has been shown to be promising in the acceleration of simulated annealing (SA) algorithms. However, benchmark Hamiltonians currently available are often characterized by the absence of a known minimum energy, making the evaluation of SA performance challenging. To address this issue, an open-source Hamiltonian generation tool based on ground-state spin logic is proposed, allowing Hamiltonians with known energy minima to be created. The tool is designed to utilize a pre-generated library of gate Hamiltonians, which are small-scale Hamiltonians representing individual logical operations (e.g., AND or OR gates), prepared through linear programming. By systematically combining these gate Hamiltonians, a target Hamiltonian can be generated to represent a larger problem. The characteristics of the target Hamiltonian, such as size and the non-zero ratio, can be customized to meet specific requirements. These Hamiltonians are evaluated using p-bit-based SA algorithms to investigate the impact of Hamiltonian properties on SA performance.