Ising Hamiltonian minimization: Gain-based computing with manifold reduction of soft-spins vs quantum annealing

We investigate the minimization of Ising Hamiltonians, comparing the performance of gain-based computing paradigms based on the dynamics of semi-classical soft-spin models with quantum an- nealing. We systematically analyze how the energy landscape for the circulant couplings of a Mo ̈bius graph evolves with increased annealing parameters. Our findings indicate that these semi-classical models face challenges due to a widening dimensionality landscape. To counteract this issue, we introduce the ‘manifold reduction’ method, which restricts the soft-spin amplitudes to a defined phase space region. Concurrently, quantum annealing demonstrates a natural capability to navigate the Ising Hamiltonian’s energy landscape due to its operation within the comprehensive Hilbert space. Our study indicates that physics-inspired or physics-enhanced optimizers will likely benefit from combining classical and quantum annealing techniques.