Universality of swap for qudits

Presenting Author: James van Meter, National Institute of Standards and Technology, Boulder
Contributing Author(s): Emanuel Knill

Using a representation theory approach, we derive conditions for which interactions with the swap Hamiltonian of qudits suffice for universal control of quantum information encoded in decoherence-free subsystems protected against all collective noise. In particular, we generalize a result of DiVincenzo et al. for the swap interactions of qubits by applying a theorem due to Marin concerning the structure of the Lie algebra generated by transpositions. As a consequence, we prove that encoded universality can also be implemented by swap interactions between three qudits, for any \(d\). Further, invoking the Littlewood-Richardson rules for tensor product decompositions, we show how any composite system of qudits can achieve encoded universality with the addition of at most \(d+1\) ancillae.

(Session 5 : Thursday from 5:00pm - 7:00 pm)


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