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References (25)
-
Martin Idel, M. Wolf (2014)
Sinkhorn normal form for unitary matricesLinear Algebra and its Applications, 471
-
A. Vos, Y. Rentergem (2008)
From Group Theory to Reversible ComputersInt. J. Unconv. Comput., 4
-
A. Barenco, C. Bennett, R. Cleve, D. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, H. Weinfurter (1995)
Elementary gates for quantum computation.Physical review. A, Atomic, molecular, and optical physics, 52 5
-
A. Vos, S. Baerdemacker (2014)
The Decomposition of U(n) into XU(n) and ZU(n)2014 IEEE 44th International Symposium on Multiple-Valued Logic
-
A. Vos, S. Baerdemacker (2014)
Scaling a Unitary MatrixOpen Syst. Inf. Dyn., 21
-
A. Vos, S. Baerdemacker (2015)
On two subgroups of U(n), useful for quantum computing, 597
-
Zahra Sasanian, D. Miller (2011)
Transforming MCT Circuits to NCVW Circuits -
A. Rae (1992)
“Grown-up” problems, real-world solutionsPhysics World, 5
-
S. Bullock, L. Markov (2003)
An Arbitrary Two-qubit Computation Elementary Gates Or Less * -
P. Selinger (2012)
Efficient Clifford+T approximation of single-qubit operatorsQuantum Inf. Comput., 15
-
R. Wille, R. Drechsler (2010)
Towards a Design Flow for Reversible Logic -
Lov Grover (2005)
What is a computer?Journal of Medical Systems, 1
-
A. Vos, J. Beule, L. Storme (2010)
Computing with the Square Root of NOTSerdica Journal of Computing
-
A. Vos, S. Baerdemacker (2014)
Matrix Calculus for Classical and Quantum CircuitsACM J. Emerg. Technol. Comput. Syst., 11
-
S. Vandenbrande, R. Laer, A. Vos (2012)
The computational power of the square root of NOT -
D. Aharonov (1998)
Quantum Computation -
E. Fredkin, T. Toffoli (2002)
Conservative logicInternational Journal of Theoretical Physics, 21
-
Nikolay Raychev, I. Chuang (2010)
Quantum Computation and Quantum Information: Bibliography -
A. Vos, S. Baerdemacker (2011)
Symmetry Groups for the Decomposition of Reversible Computers, Quantum Computers, and Computers in betweenSymmetry, 3
-
A. Galindo, M. Martin-Delgado (2001)
Information and computation: Classical and quantum aspectsReviews of Modern Physics, 74
-
M. Amy, D. Maslov, M. Mosca (2013)
Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid PartitioningIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 33
-
T. Beth, M. Rötteler (2001)
Quantum Algorithms: Applicable Algebra and Quantum Physics, 173
-
Member Soeken, Member Wille, Student Keszocze, M. Miller, Senior Drechsler (2014)
Embedding of Large Boolean Functions for Reversible LogicACM Journal on Emerging Technologies in Computing Systems (JETC), 12
-
A. Vos, S. Baerdemacker (2013)
The NEGATOR as a Basic Building Block for Quantum CircuitsOpen Syst. Inf. Dyn., 20
-
R. Hermann, L. Biedenharn (1967)
Lie Groups for PhysicistsPhysics Today, 20
- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing Switzerland 2017
- ISBN
- 978-3-319-33923-8
- Pages
- 455 –474
- DOI
- 10.1007/978-3-319-33924-5_18
- Publisher site
- See Chapter on Publisher Site
Abstract
[By systematically inflating the group of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \times n$$\end{document} permutation matrices to the group of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \times n$$\end{document} unitary matrices, we can see how classical computing is embedded in quantum computing. In this process, an important role is played by two subgroups of the unitary group U(n), i.e. XU(n) and ZU(n). Here, XU(n) consists of all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \times n$$\end{document} unitary matrices with all line sums (i.e. the n row sums and the n column sums) equal to 1, whereas ZU(n) consists of all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \times n$$\end{document} diagonal unitary matrices with upper-left entry equal to 1. As a consequence, quantum computers can be built from NEGATOR gates and PHASOR gates. The NEGATOR is a 1-qubit circuit that is a natural generalization of the 1-bit NOT gate of classical computing. In contrast, the PHASOR is a 1-qubit circuit not related to classical computing.]
Published: Jul 19, 2016