ON SWAPPING THE STATES OF TWO QUDITS
Colin Wilmott · International Journal of Quantum Information · 2011
The SWAP gate has become an integral component of quantum circuit architecture where its primary role is given to permuting the states of two qubits. We consider the question of whether a two-qudit quantum circuit composed entirely from instances of the generalized controlled-NOT gate can be constructed to permute the states of two qudits. Arguing via the signature of a permutation, we demonstrate the impossibility of such circuits for dimensions d ≡ 3 (mod 4).