Explicit controlled-SWAP variational circuits generate exact uniform permutation distributions on linear nearest-neighbor topologies in O(n) depth, while Beneš-like architectures cannot produce uniform distributions for any parameter choice.
Random sampling of permutations using quantum circuits.IEEE Transactions on Computer-Aided De- sign of Integrated Circuits and Systems, 45(2):631–644, 2026
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Variational Approach for Uniform Quantum Permutation Generators
Explicit controlled-SWAP variational circuits generate exact uniform permutation distributions on linear nearest-neighbor topologies in O(n) depth, while Beneš-like architectures cannot produce uniform distributions for any parameter choice.