Cyclic groups and quantum logic gates

被引：2

作者：

Pourkia, Arash ^{[1
]}

Batle, J. ^{[2
]}

机构：

[1] Amer Univ Middle East, Coll Engn, Div Math, 220 Dasman, Kuwait 15453, Kuwait

[2] Univ Illes Balears, Dept Fis, Palma De Mallorca, Balearic Island, Spain

来源：

ANNALS OF PHYSICS | 2016年 / 373卷

关键词：

Quantum computation; Yang-Baxter equation; Quantum gates; Cyclic groups; Berry phase; YANG-BAXTER EQUATION; STATE;

D O I：

10.1016/j.aop.2016.06.023

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present a formula for an infinite number of universal quantum logic gates, which are 4 by 4 unitary solutions to the Yang-Baxter (Y-B) equation. We obtain this family from a certain representation of the cyclic group of order n. We then show that this discrete family, parametrized by integers n, is in fact, a small sub-class of a larger continuous family, parametrized by real numbers 9, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：10 / 27

页数：18

共 31 条

[1] Barenco A., 1937, P MATH PHYS SCI, V449, P679
[2] COMMUNICATION VIA ONE-PARTICLE AND 2-PARTICLE OPERATORS ON EINSTEIN-PODOLSKY-ROSEN STATES
BENNETT, CH
WIESNER, SJ
[J]. PHYSICAL REVIEW LETTERS, 1992, 69 (20) : 2881 - 2884
[3] TELEPORTING AN UNKNOWN QUANTUM STATE VIA DUAL CLASSICAL AND EINSTEIN-PODOLSKY-ROSEN CHANNELS
BENNETT, CH
BRASSARD, G
CREPEAU, C
JOZSA, R
PERES, A
WOOTTERS, WK
[J]. PHYSICAL REVIEW LETTERS, 1993, 70 (13) : 1895 - 1899
[4] Berman G P., 1998, Introduction to Quantum Computers
[5] Brylinski J.L., 2002, MATH QUANTUM COMPUTA
[6] Braiding transformation, entanglement swapping, and Berry phase in entanglement space
Chen, Jing-Ling
Xue, Kang
Ge, Mo-Lin
[J]. PHYSICAL REVIEW A, 2007, 76 (04):
[7] YANG-BAXTERIZATION OF BRAID GROUP-REPRESENTATIONS
CHENG, Y
GE, ML
XUE, K
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 136 (01) : 195 - 208
[8] Chuang I. N., 2000, Quantum Computation and Quantum Information
[9] Unitary Solutions to the Yang-Baxter Equation in Dimension Four
Dye, H. A.
[J]. QUANTUM INFORMATION PROCESSING, 2003, 2 (1-2) : 117 - 151
[10] Quantum computation and Shor's factoring algorithm
Ekert, A
Jozsa, R
[J]. REVIEWS OF MODERN PHYSICS, 1996, 68 (03) : 733 - 753

← 1 2 3 4 →