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

Dylan Laplace Mermoud, Andrea Simonetto, and Sourour Elloumi, Quantum 10, 1998 (2026). 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.