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The group of dyadic unitary matrices

Alexis De Vos UGent, Raphaël Van Laer UGent and Steven Vandenbrande (2012) OPEN SYSTEMS & INFORMATION DYNAMICS. 19(1). p.1-28
abstract
We introduce the group DU(m) of m x m dyadic unitary matrices, i.e. unitary matrices with all entries having a real and an imaginary part that are both rational numbers with denominator of the form 2(p) (with p a non-negative integer). We investigate in detail the finite groups DU(1) and DU(2) and the discrete, but infinite groups DU(3) and DU(4). We further introduce the subgroup XDU(m) of DU(m), consisting of those members of DU(m) that have constant line sum 1. The study of XDU(2) and XDU(4) leads to conclusions concerning the synthesis of quantum computers acting on one and two qubits, respectively.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
quantum computing, unitary matrix, COMPUTATION
journal title
OPEN SYSTEMS & INFORMATION DYNAMICS
Open Syst. Inf. Dyn.
volume
19
issue
1
article_number
1250003
pages
1 - 28
Web of Science type
Article
Web of Science id
000304831600003
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.898 (2012)
JCR rank
89/247 (2012)
JCR quartile
2 (2012)
ISSN
1230-1612
DOI
10.1142/S1230161212500035
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2069554
handle
http://hdl.handle.net/1854/LU-2069554
date created
2012-03-19 17:58:18
date last changed
2012-10-26 14:07:12
@article{2069554,
  abstract     = {We introduce the group DU(m) of m x m dyadic unitary matrices, i.e. unitary matrices with all entries having a real and an imaginary part that are both rational numbers with denominator of the form 2(p) (with p a non-negative integer). We investigate in detail the finite groups DU(1) and DU(2) and the discrete, but infinite groups DU(3) and DU(4). We further introduce the subgroup XDU(m) of DU(m), consisting of those members of DU(m) that have constant line sum 1. The study of XDU(2) and XDU(4) leads to conclusions concerning the synthesis of quantum computers acting on one and two qubits, respectively.},
  articleno    = {1250003},
  author       = {De Vos, Alexis and Van Laer, Rapha{\"e}l and Vandenbrande, Steven},
  issn         = {1230-1612},
  journal      = {OPEN SYSTEMS \& INFORMATION DYNAMICS},
  keyword      = {quantum computing,unitary matrix,COMPUTATION},
  language     = {eng},
  number       = {1},
  pages        = {1250003:1--1250003:28},
  title        = {The group of dyadic unitary matrices},
  url          = {http://dx.doi.org/10.1142/S1230161212500035},
  volume       = {19},
  year         = {2012},
}

Chicago
De Vos, Alexis, Raphaël Van Laer, and Steven Vandenbrande. 2012. “The Group of Dyadic Unitary Matrices.” Open Systems & Information Dynamics 19 (1): 1–28.
APA
De Vos, Alexis, Van Laer, R., & Vandenbrande, S. (2012). The group of dyadic unitary matrices. OPEN SYSTEMS & INFORMATION DYNAMICS, 19(1), 1–28.
Vancouver
1.
De Vos A, Van Laer R, Vandenbrande S. The group of dyadic unitary matrices. OPEN SYSTEMS & INFORMATION DYNAMICS. 2012;19(1):1–28.
MLA
De Vos, Alexis, Raphaël Van Laer, and Steven Vandenbrande. “The Group of Dyadic Unitary Matrices.” OPEN SYSTEMS & INFORMATION DYNAMICS 19.1 (2012): 1–28. Print.