Abstract
Robert Ainsworth (NUI Maynooth)
Topological Qubit Design and Leakage
We examine how best to design qubits for use in topological quantum
computation. These qubits are topological Hilbert spaces associated with
small groups of anyons. Op- erations are performed on these by exchanging
the anyons. One might argue that, in order to have as many simple single
qubit operations as possible, the number of anyons per group should be
maximized. However, we show that there is a maximal number of particles
per qubit, namely 4, and more generally a maximal number of particles for
qudits of dimension d. We also look at the possibility of having
topological qubits for which one can perform two-qubit gates without
leakage into non-computational states. It turns out that the requirement
that all two-qubit gates are leakage free is very restrictive and this
property can only be realized for two-qubit systems related to Ising-like
anyon models, which do not allow for universal quantum computation by
braiding. Our results follow directly from the representation theory of
braid groups which means they are valid for all anyon models. We also make
some remarks on generalizations to other exchange groups.
This work has been published in New J.Phys.13:065030, 2011. See also
arxiv:1102.5029