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arXiv · 2311.17359

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

James S. Cummins·Hayder Salman·Natalia G. Berloff
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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.

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James S. Cummins, Hayder Salman, Natalia G. Berloff. 2023-11-29. Ising Hamiltonian Minimization: Gain-Based Computing with Manifold Reduction of Soft-Spins vs Quantum Annealing. https://doi.org/10.1103/physrevresearch.7.013150

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