Fully Connected Ising Machine with Fully Parallel Spin Updates Based on Discrete Field-Induced Bifurcation for Combinatorial Optimization

Combinatorial optimization is fundamental to domains such as machine learning, logistics, and network design. However, many of these problems are NP-hard, posing a significant challenge to classical von Neumann architectures. As a promising alternative, Ising machines map these problems to spin systems and solve them by minimizing the Ising Hamiltonian. Fully connected Ising topologies are particularly desirable, as they enable direct and lossless problem mapping. Yet, most existing hardware implementations either suffer from limited connectivity or rely on complex mechanisms such as spin replication or differential equation solving, which hinder scalability and efficiency. In this work, we propose a novel Discrete Field-Induced Bifurcation (DFIB) method that enables fully parallel spin updates without spin duplication. Unlike simulated bifurcation approaches that require solving large differential systems, DFIB employs a simplified update rule based on multiply-accumulate (MAC) operations, enabling low-complexity, scalable hardware implementation. To further improve solution quality, a lightweight periodic random masking strategy is introduced to escape local minima. We also present a RRAM-based current-branching architecture for efficient local field computation, which supports high weight precision and mitigates current overload issues common in in-memory computing. Simulation results on 100-node fully connected Max-Cut problems show that DFIB achieves up to 98% of optimal solution quality, with time-to-solution ranging from 0.14us to 3.4us, depending on graph density. In dense graphs, convergence to 95% of the optimum is achieved within 10 iterations, even without perturbation. These results demonstrate DFIB’s superior speed, accuracy, and scalability for large-scale combinatorial optimization.