Howard, Mark and Vala, Jiri (2012) Nonlocality as a benchmark for universal quantum computation in Ising anyon topological quantum computers. Physical Review A (022304). pp. 1-7. ISSN 1050-2947

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Abstract

An obstacle affecting any proposal for a topological quantum computer based on Ising anyons is that quasiparticle braiding can only implement a finite (nonuniversal) set of quantum operations. The computational power of this restricted set of operations (often called stabilizer operations) has been studied in quantum information theory, and it is known that no quantum-computational advantage can be obtained without the help of an additional nonstabilizer operation. Similarly, a bipartite two-qubit system based on Ising anyons can not exhibit nonlocality (in the sense of violating a Bell inequality) when only topologically protected stabilizer operations are performed. To produce correlations that can not be described by a local hidden variable model again requires the use of a nonstabilizer operation. Using geometric techniques, we relate the sets of operations that enable universal quantum computing (UQC) with those that enable violation of a Bell inequality. Motivated by the fact that nonstabilizer operations are expected to be highly imperfect, our aim is to provide a benchmark for identifying UQC-enabling operations that is both experimentally practical and conceptually simple.We show that any (noisy) single-qubit nonstabilizer operation that, together with perfect stabilizer operations, enables violation of the simplest two-qubit Bell inequality, can also be used to enable UQC. This benchmarking requires finding the expectation values of two distinct Pauli measurements on each qubit of a bipartite system.

Item Type:	Article
Additional Information:	The definitive version of this article is available at DOI: 10.1103/PhysRevA.85.022304 . We thank E. Campbell for helpful comments on a previous version of this manuscript. M.H. was supported by the Irish Research Council for Science, Engineering and Technology (IRCSET) as an Empower Fellow. J.V. acknowledges funding from Science Foundation Ireland under Grant No. SFI 10/IN.1/I3013.
Keywords:	Nonlocality; universal quantum computation; Ising anyon; topological quantum computers;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	4504
Depositing User:	Dr. Jiri Vala
Date Deposited:	18 Sep 2013 15:52
Journal or Publication Title:	Physical Review A
Publisher:	American Physical Society
Refereed:	Yes
URI:	http://pra.aps.org/
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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