Ainsworth, Robert and Slingerland, Joost
(2011)
Topological qubit design and leakage.
New Journal of Physics (NJP), 13.
065030.
ISSN 1367-2630
Abstract
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. Operations 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 implies that they are valid for all anyon models.
We also make some remarks about generalizations to other exchange groups.
Item Type: |
Article
|
Keywords: |
Topological qubit design; leakage; |
Academic Unit: |
Faculty of Science and Engineering > Mathematical Physics |
Item ID: |
4797 |
Depositing User: |
Dr. Joost Slingerland
|
Date Deposited: |
05 Mar 2014 16:57 |
Journal or Publication Title: |
New Journal of Physics (NJP) |
Publisher: |
Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft |
Refereed: |
Yes |
URI: |
|
Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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