Clifford gates by code deformation

被引：54

作者：

Bombin, H. ^{[1
]}

机构：

[1] Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada

来源：

NEW JOURNAL OF PHYSICS | 2011年 / 13卷

关键词：

ERROR-CORRECTING CODES; QUANTUM; MEMORY;

D O I：

10.1088/1367-2630/13/4/043005

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Topological subsystem color codes add an important feature to the advantages of topological codes: error tracking only involves measuring two local operators in a two-dimensional setting. Unfortunately, currently known methods for computing with them are highly unpractical. We give a mechanism for implementing all Clifford gates by code deformation in a planar setting. In particular, we use twist braiding and express its effects in terms of certain colored Majorana operators.

引用

页数：13

共 27 条

[11] BRAVYI S, 2010, ARXIV10043791
[12] BRAVYI S, 2010, ARXIV10081029
[13] Tradeoffs for Reliable Quantum Information Storage in 2D Systems
Bravyi, Sergey
Poulin, David
Terhal, Barbara
[J]. PHYSICAL REVIEW LETTERS, 2010, 104 (05)
[14] Topological quantum memory
Dennis, E
Kitaev, A
Landahl, A
Preskill, J
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (09) : 4452 - 4505
[15] Fast Decoders for Topological Quantum Codes
Duclos-Cianci, Guillaume
Poulin, David
[J]. PHYSICAL REVIEW LETTERS, 2010, 104 (05)
[16] Projective plane and planar quantum codes
Freedman, MH
Meyer, DA
[J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2001, 1 (03) : 325 - 332
[17] Class of quantum error-correcting codes saturating the quantum Hamming hound
Gottesman, D
[J]. PHYSICAL REVIEW A, 1996, 54 (03): : 1862 - 1868
[18] Error Threshold for Color Codes and Random Three-Body Ising Models
Katzgraber, Helmut G.
Bombin, H.
Martin-Delgado, M. A.
[J]. PHYSICAL REVIEW LETTERS, 2009, 103 (09)
[19] Fault-tolerant quantum computation by anyons
Kitaev, AY
[J]. ANNALS OF PHYSICS, 2003, 303 (01) : 2 - 30
[20] Unified and generalized approach to quantum error correction
Kribs, D
Laflamme, R
Poulin, D
[J]. PHYSICAL REVIEW LETTERS, 2005, 94 (18)

← 1 2 3 →