Scheme for fault-tolerant holonomic computation on stabilizer codes

Ognyan Oreshkov, Todd A. Brun, and Daniel A. Lidar

Phys. Rev. A 80, 022325 – Published 19 August 2009

Abstract

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.

Received 14 April 2009

DOI:https://doi.org/10.1103/PhysRevA.80.022325

Authors & Affiliations

Ognyan Oreshkov^1,2,3, Todd A. Brun^2,3,4, and Daniel A. Lidar^2,3,4,5

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

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 80, Iss. 2 — August 2009

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Physical Review A

covering atomic, molecular, and optical physics and quantum information