C[subscript 3], semi-clifford and generalized semi-clifford operations
Name
Shor_C3 Semi.pdf
Size
217.74 KB
Format
Adobe PDF
Checksum (MD5)
fae55131be9b419ba4fe6db339908fa1
Author(s)
Beigi, Salman
Shor, Peter W.
Date Issued
January 2010
Journal
Quantum Information & Computation
Publisher
Rinton Press
Citation
Salman Beigi and Peter W. Shor. 2010. C3, semi-clifford and generalized semi-clifford operations. Quantum Info. Comput. 10, 1 (January 2010), 41-59.
Version
Author's final manuscript
Abstract
Fault-tolerant quantum computation is a basic problem in quantum computation, andteleportation is one of the main techniques in this theory. Using teleportation on stabi-lizer codes, the most well-known quantum codes, Pauli gates and Clifford operators canbe applied fault-tolerantly. Indeed, this technique can be generalized for an extended setof gates, the so called Ck hierarchy gates, introduced by Gottesman and Chuang (Nature,402, 390-392). Ck gates are a generalization of Clifford operators, but our knowledge ofthese sets is not as rich as our knowledge of Clifford gates. Zeng et al. in (Phys. Rev.A 77, 042313) raise the question of the relation between Ck hierarchy and the set ofsemi-Clifford and generalized semi-Clifford operators. They conjecture that any Ck gateis a generalized semi-Clifford operator. In this paper, we prove this conjecture for k = 3.Using the techniques that we develop, we obtain more insight on how to characterize Ckgates. Indeed, the more we understand Ck, the more intuition we have on Ck, k ≥ 4, and then we have a way of attacking the conjecture for larger k.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
http://dl.acm.org/citation.cfm?id=2011442
