Ising Hamiltonian Minimization: Gain-Based Computing with Manifold Reduction of Soft-Spins vs Quantum Annealing

Abstract

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 annealing. We systematically analyze how the energy landscape for the circulant couplings of a Mobius 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.

12 pages, 12 figures; published by Phys. Rev. Research 7, 013150 (2025)

References in corpus (23)

• Large-scale photonic Ising machine by spatial light modulation
• Realizing the $XY$ Hamiltonian in polariton simulators
• Experimental investigation of performance differences between Coherent Ising Machines and a quantum annealer
• Quantum critical dynamics in a 5000-qubit programmable spin glass
• Coherent quantum annealing in a programmable 2000-qubit Ising chain
• Demonstration of a scaling advantage for a quantum annealer over simulated annealing
• Quantum versus Classical Annealing of Ising Spin Glasses
• Efficient Quantum Walk on a Quantum Processor
• Dissipative phase locking of exciton-polariton condensates
• Tunneling and speedup in quantum optimization for permutation-symmetric problems
• Simulating Ising and Potts models and external fields with non-equilibrium condensates
• Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
• Networks of non-equilibrium condensates for global optimization
• Realizing spin-Hamiltonians in nanoscale active photonic lattices
• Entanglement and replica symmetry breaking in a driven-dissipative quantum spin glass
• Rapid fair sampling of XY spin Hamiltonian with a laser simulator
• All-optical scalable spatial coherent Ising machine
• Controllable Josephson junction for photon Bose-Einstein condensates
• The Wishart planted ensemble: A tunably-rugged pairwise Ising model with a first-order phase transition
• Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian
• Coding closed and open quantum systems in MATLAB: applications in quantum optics and condensed matter
• Noise amplification at spin-glass bottlenecks of quantum annealing: a solvable model
• Critical parameters of the synchronisation's stability for coupled maps in regular graphs