### Reversible computation, quantum computation, and computer architectures in between

(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:
http://hdl.handle.net/1854/LU-1002740

- author
- Alexis De Vos UGent, Michiel Boes UGent and Stijn De Baerdemacker UGent
- organization
- year
- 2010
- 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.