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Q: Fachverband Quantenoptik und Photonik

Q 5: Quanteninformation: Konzepte I

Q 5.7: Talk

Monday, March 2, 2009, 12:15–12:30, VMP 6 HS-D

On Quantum Qudit Gate Constructions — •Colin Wilmott — School of Mathematical Sciences, University College Dublin, Dublin, Ireland — Institut für Theoretische Physik III, Heinrich-Heine-Universität, Düsseldorf, Deutschland

Most often it is assumed that quantum computations are predicated on a collection of 2-level quantum mechanical systems called qubits. However, there is a view to generalise to d-level, or qudit, quantum mechanical systems. Furthermore, it is becoming increasingly evident that much effort continues to be made into finding efficient quantum networks in the sense that for the given gate library there is no smaller network that achieves the same task.

The qubit SWAP gate has been illustrated to be a cornerstone in the networkability of quantum computation based on qubits. We introduce a quantum gate construction that generalises the qubit SWAP gate to higher dimensions. This construction makes extensive use of binomial summations and yields a quantum qudit SWAP gate determined only in the CNOT gate. In addition, the task of constructing generalised SWAP gates based on transpositions of qudit states is argued in terms of the signature of a permutation.