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arXiv · 1101.4159

On swapping the states of two qudits

Colin Wilmott
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Abstract

The SWAP gate has become an integral feature of quantum circuit architectures and is designed to permute the states of two qubits through the use of the well-known controlled-NOT gate. We consider the question of whether a two-qudit quantum circuit composed entirely from instances of the generalised 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 $d \equiv 3$ (mod 4).

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Colin Wilmott. 2011-01-21. On swapping the states of two qudits. https://arxiv.org/abs/1101.4159

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