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arXiv · 2505.05981

Variational quantum algorithms for permutation-based combinatorial problems: Optimal ansatz generation with applications to quadratic assignment problems and beyond

Dylan Laplace Mermoud·Andrea Simonetto·Sourour Elloumi
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Abstract

We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most importantly the Bruhat decomposition of the group generated by the \(\mathtt{cx}\) gates. These circuits require a number of qubits that scale logarithmically with the permutation dimension, and are therefore employable in near-term applications. We further augment the circuits with ancilla qubits to enlarge their span, and with these we build ansatze to tackle permutation-based optimization problems such as quadratic assignment problems, and graph isomorphisms. The resulting quantum algorithm, \textsc{QuPer}, is competitive with respect to classical heuristics and we could simulate its behavior up to a problem with $256$ variables, requiring $20$ qubits.

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Dylan Laplace Mermoud, Andrea Simonetto, Sourour Elloumi. 2025-05-09. Variational quantum algorithms for permutation-based combinatorial problems: Optimal ansatz generation with applications to quadratic assignment problems and beyond. https://doi.org/10.22331/q-2026-02-09-1998

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