A reduction scheme for general-order Ising-like Hamiltonians in quantum heuristic solvers

Abstract:The Ising model is ubiquitous in various optimization problems but notoriously difficult to solve due to combinatorial explosion. In view of this, Hamiltonian reduction is a useful preprocessing technique for reducing the effective problem size before applying heuristic solvers. However, existing reduction techniques mainly target second-order Ising models, whereas many pseudo-Boolean formulations naturally contain higher-order interactions. In this work, we generalize the concept of non-separable groups to arbitrary-order Ising-like models and develop a Hamiltonian reduction framework that iteratively detects and merges constrained spin groups into single variables. We benchmark the reduction on synthetic hypergraphs and higher-order network datasets, and evaluate its integration with downstream order-reduction and solver workflows. Our results establish a foundation for Hamiltonian reduction in higher-order Ising-like optimization problems.

arXiv:2607.19871 [quant-ph]

(or arXiv:2607.19871v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.19871 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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