High-Parallel FPGA-Based Discrete Simulated Bifurcation for Large-Scale Optimization

Abstract: Combinatorial Optimization (CO) problems exhibit exponential complexity, making their resolution challenging. Simulated Adiabatic Bifurcation (aSB) is a quantum-inspired algorithm to obtain approximate solutions to largescale CO problems written in the Ising form. It explores the solution space by emulating the adiabatic evolution of a network of Kerr-nonlinear parametric oscillators (KPOs), where each oscillator represents a variable in the problem. The optimal solution corresponds to the ground state of this system. A key advantage of this approach is the possibility of updating multiple variables simultaneously, making it particularly suited for hardware implementation. To enhance solution quality and convergence speed, variations of the algorithm have been proposed in the literature, including ballistic (bSB), discrete (dSB), and thermal (HbSB) versions. In this work, we have comprehensively analyzed dSB, bSB, and HbSB using dedicated software models, evaluating the feasibility of using a fixed-point representation for hardware implementation. We then present an opensource hardware architecture implementing the dSB algorithm for Field-Programmable Gate Arrays (FPGAs). The design allows users to adjust the degree of algorithmic parallelization based on their specific requirements. A proof-of-concept implementation that solves 256-variable problems was achieved on an AMD Kria KV260 SoM, a low-tier FPGA, validated using well-known max-cut and knapsack problems.