A fermionic permutation protocol on 2D nearest-neighbor grids achieves the optimal O(sqrt(N)) depth with O(N sqrt(N)) gates, no ancillas, and extends to Jordan-Wigner, Bravyi-Kitaev, and Parity encodings via Hilbert-curve layout.
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Asymptotically Optimal Depth Fermionic Permutation on 2D Grid Quantum Architecture without Ancillas
A fermionic permutation protocol on 2D nearest-neighbor grids achieves the optimal O(sqrt(N)) depth with O(N sqrt(N)) gates, no ancillas, and extends to Jordan-Wigner, Bravyi-Kitaev, and Parity encodings via Hilbert-curve layout.