## Abstracts

### 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)

SQuInT Chief Organizer
Akimasa Miyake, Assistant Professor
amiyake@unm.edu

SQuInT Co-Organizer
Mark M. Wilde, Assistant Professor LSU
mwilde@phys.lsu.edu