On interchanging the states of a pair of qudits

Details On interchanging the states of a pair of qudits On interchanging the states of a pair of qudits

2008-11-10

arxiv.org/abs/0811.1545v1

Physics

Quantum Physics

4 pages, 3 figures

Scientific paper

The qubit SWAP gate has been shown to be an integral component of quantum circuitry design. It permutes the states of two qubits and allows for the storage quantum information, teleportation of atomic or ionic states, and is a fundamental element in the circuit implementation of Shor's algorithm. We consider the problem of generalising the SWAP gate beyond the qubit setting. We show that quantum circuit architectures completely described by instances of the CNOT gate can not implement a transposition of a pair of qudits for dimensions $d \equiv 3 (mod 4)$. The task of constructing generalised SWAP gates based on transpositions of qudit states is argued in terms of the signature of a permutation.

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