Efficient computations of encodings for quantum error correction

被引:66
作者
Cleve, R [1 ]
Gottesman, D [1 ]
机构
[1] CALTECH, PASADENA, CA 91125 USA
来源
PHYSICAL REVIEW A | 1997年 / 56卷 / 01期
关键词
D O I
10.1103/PhysRevA.56.76
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We show how, given any set of generators of the stabilizer of a quantum code, an efficient gate array that computes the code words can be explicitly constructed. For an n-qubit code whose stabilizer has d generators, the resulting gate array consists of O(nd) operations, and converts k-qubit data (where k = n-d) into n-qubit code words.
引用
收藏
页码:76 / 82
页数:7
相关论文
共 16 条
[1]   ELEMENTARY GATES FOR QUANTUM COMPUTATION [J].
BARENCO, A ;
BENNETT, CH ;
CLEVE, R ;
DIVINCENZO, DP ;
MARGOLUS, N ;
SHOR, P ;
SLEATOR, T ;
SMOLIN, JA ;
WEINFURTER, H .
PHYSICAL REVIEW A, 1995, 52 (05) :3457-3467
[2]  
Bennett CH, 1996, PHYS REV A, V54, P3824, DOI 10.1103/PhysRevA.54.3824
[3]   Perfect quantum-error-correction coding in 24 laser pulses [J].
Braunstein, SL ;
Smolin, JA .
PHYSICAL REVIEW A, 1997, 55 (02) :945-950
[4]   Good quantum error-correcting codes exist [J].
Calderbank, AR ;
Shor, PW .
PHYSICAL REVIEW A, 1996, 54 (02) :1098-1105
[5]   Quantum-error correction and orthogonal geometry [J].
Calderbank, AR ;
Rains, EM ;
Shor, PW ;
Sloane, NJA .
PHYSICAL REVIEW LETTERS, 1997, 78 (03) :405-408
[6]  
CALDERBANK AR, UNPUB
[7]   Fault-tolerant error correction with efficient quantum codes [J].
DiVincenzo, DP ;
Shor, PW .
PHYSICAL REVIEW LETTERS, 1996, 77 (15) :3260-3263
[8]   Quantum error correction for communication [J].
Ekert, A ;
Macchiavello, C .
PHYSICAL REVIEW LETTERS, 1996, 77 (12) :2585-2588
[9]   Class of quantum error-correcting codes saturating the quantum Hamming hound [J].
Gottesman, D .
PHYSICAL REVIEW A, 1996, 54 (03) :1862-1868
[10]   Theory of quantum error-correcting codes [J].
Knill, E ;
Laflamme, R .
PHYSICAL REVIEW A, 1997, 55 (02) :900-911