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.
Frequency hopping spread spectrum: History, principles and applications.Military Technical Courier, 70:856–876, 10 2022
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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.