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Reversible computation, quantum computation, and computer architectures in between

Alexis De Vos UGent, Michiel Boes UGent and Stijn De Baerdemacker UGent (2010) Reversible Computation, 2nd Workshop, Proceedings. p.75-81
abstract
Thanks to the cosine-sine decomposition of unitary matrices, an arbitrary quantum circuit, acting on w qubits, can be decomposed into 2^w-1 elementary quantum gates, called controlled V gates. Thanks to the Birkhoff decomposition of doubly stochastic matrices, an arbitrary (classical) reversible circuit, acting on w bits, can be decomposed into 2w-1 elementary gates, called controlled NOT gates. The question arises under which conditions these two synthesis methods are applicable for intermediate cases, i.e. computers based on some group, which simultaneously is a subgroup of the unitary group U(2^w) and a supergroup of the symmetric group S_{2^w}. It turns out that many groups either belong to a class that might have a cosine-sine-like decomposition but no Birkhoff-like decomposition and a second class that might have both decompositions. For an arbitrary group, in order to find out to which class it belongs, it suffices to evaluate a function Phi(m), deduced either from its order (in case of a finite group) or from its dimension (in case of a Lie group). Here m=2^w is the degree of the group.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
keyword
quantum computation, group theory, reversible computation
in
Reversible Computation, 2nd Workshop, Proceedings
editor
Rolf Drechsler
pages
75 - 81
publisher
Universität Bremen
place of publication
Bremen, Germany
conference name
2nd Workshop on Reversible Computation (RC 2010)
conference location
Bremen, Germany
conference start
2010-07-02
conference end
2010-07-03
language
English
UGent publication?
yes
classification
C1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1002740
handle
http://hdl.handle.net/1854/LU-1002740
date created
2010-07-06 08:00:20
date last changed
2010-08-13 13:00:35
@inproceedings{1002740,
  abstract     = {Thanks to the cosine-sine decomposition of unitary matrices, an arbitrary quantum circuit, acting on w qubits, can be decomposed into 2\^{ }w-1 elementary quantum gates, called controlled V gates. Thanks to the Birkhoff decomposition of doubly stochastic matrices, an arbitrary (classical) reversible circuit, acting on w bits, can be decomposed into 2w-1 elementary gates, called controlled NOT gates.
The question arises under which conditions these two synthesis methods are applicable for intermediate cases, i.e.  computers based on some group, which simultaneously is a subgroup of the unitary group U(2\^{ }w) and a supergroup of the symmetric group S\_\{2\^{ }w\}. It turns out that many groups either belong to a class that might have a cosine-sine-like decomposition but no Birkhoff-like decomposition and a second class that might have both decompositions.
For an arbitrary group, in order to find out to which class it belongs, it suffices to evaluate a function Phi(m), deduced 
either from its order  (in case of a finite group) or from its dimension (in case of a Lie group). Here m=2\^{ }w is the degree of the group.},
  author       = {De Vos, Alexis and Boes, Michiel and De Baerdemacker, Stijn},
  booktitle    = {Reversible Computation, 2nd Workshop, Proceedings},
  editor       = {Drechsler, Rolf},
  keyword      = {quantum computation,group theory,reversible computation},
  language     = {eng},
  location     = {Bremen, Germany},
  pages        = {75--81},
  publisher    = {Universit{\"a}t Bremen},
  title        = {Reversible computation, quantum computation, and computer architectures in between},
  year         = {2010},
}

Chicago
De Vos, Alexis, Michiel Boes, and Stijn De Baerdemacker. 2010. “Reversible Computation, Quantum Computation, and Computer Architectures in Between.” In Reversible Computation, 2nd Workshop, Proceedings, ed. Rolf Drechsler, 75–81. Bremen, Germany: Universität Bremen.
APA
De Vos, Alexis, Boes, M., & De Baerdemacker, S. (2010). Reversible computation, quantum computation, and computer architectures in between. In R. Drechsler (Ed.), Reversible Computation, 2nd Workshop, Proceedings (pp. 75–81). Presented at the 2nd Workshop on Reversible Computation (RC 2010), Bremen, Germany: Universität Bremen.
Vancouver
1.
De Vos A, Boes M, De Baerdemacker S. Reversible computation, quantum computation, and computer architectures in between. In: Drechsler R, editor. Reversible Computation, 2nd Workshop, Proceedings. Bremen, Germany: Universität Bremen; 2010. p. 75–81.
MLA
De Vos, Alexis, Michiel Boes, and Stijn De Baerdemacker. “Reversible Computation, Quantum Computation, and Computer Architectures in Between.” Reversible Computation, 2nd Workshop, Proceedings. Ed. Rolf Drechsler. Bremen, Germany: Universität Bremen, 2010. 75–81. Print.