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Universal Fault-Tolerant Quantum Computation with Only Transversal Gates <?format ?>and Error Correction

Universal Fault-Tolerant Quantum Computation with Only Transversal Gates and Error... Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. Though transversal gates alone cannot be computationally universal, they can be combined with specially distilled resource states in order to achieve universality. We show that “triorthogonal” stabilizer codes, introduced for state distillation by Bravyi and Haah ( Phys. Rev. A 86 , 052329 ( 2012 ) ), admit transversal implementation of the controlled-controlled- Z gate. We then construct a universal set <?format ?>of fault-tolerant gates without state distillation by using only transversal controlled-controlled- Z , transversal Hadamard, and fault-tolerant error correction. We also adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Letters American Physical Society (APS)

Universal Fault-Tolerant Quantum Computation with Only Transversal Gates <?format ?>and Error Correction

Physical Review Letters , Volume 111 (9) – Aug 30, 2013
5 pages

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Publisher
American Physical Society (APS)
Copyright
Copyright © 2013 The American Physical Society
ISSN
1079-7114
DOI
10.1103/PhysRevLett.111.090505
pmid
24033013
Publisher site
See Article on Publisher Site

Abstract

Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. Though transversal gates alone cannot be computationally universal, they can be combined with specially distilled resource states in order to achieve universality. We show that “triorthogonal” stabilizer codes, introduced for state distillation by Bravyi and Haah ( Phys. Rev. A 86 , 052329 ( 2012 ) ), admit transversal implementation of the controlled-controlled- Z gate. We then construct a universal set <?format ?>of fault-tolerant gates without state distillation by using only transversal controlled-controlled- Z , transversal Hadamard, and fault-tolerant error correction. We also adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes.

Journal

Physical Review LettersAmerican Physical Society (APS)

Published: Aug 30, 2013

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