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Phys. Rev. A 80, 022325 (2009) [17 pages]

Scheme for fault-tolerant holonomic computation on stabilizer codes

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Ognyan Oreshkov1,2,3, Todd A. Brun2,3,4, and Daniel A. Lidar2,3,4,5
1Grup de Física Teòrica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona 08193, Spain
2Department of Physics, University of Southern California, Los Angeles, California 90089, USA
3Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
4Communication Science Institute, University of Southern California, Los Angeles, California 90089, USA
5Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA

Received 14 April 2009; published 19 August 2009

This paper generalizes and expands upon the work [ O. Oreshkov, T. A. Brun and D. A. Lidar Phys. Rev. Lett. 102 070502 (2009)] where we introduced a scheme for fault-tolerant holonomic quantum computation (HQC) on stabilizer codes. HQC is an all-geometric strategy based on non-Abelian adiabatic holonomies, which is known to be robust against various types of errors in the control parameters. The scheme we present shows that HQC is a scalable method of computation and opens the possibility for combining the benefits of error correction with the inherent resilience of the holonomic approach. We show that with the Bacon-Shor code the scheme can be implemented using Hamiltonian operators of weights 2 and 3.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.80.022325
DOI:
10.1103/PhysRevA.80.022325
PACS:
03.67.Pp, 03.65.Vf
 
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