### Symmetry groups for the decomposition of reversible computers, quantum computers, and computers in between

(2011) SYMMETRY-BASEL. 3(2). p.305-324- abstract
- Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e. the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with w bits and the decomposition of an arbitrary quantum circuit with w qubits. Both decompositions use the control gate as building block, i.e. a circuit transforming only one (qu)bit, the transformation being controlled by the other w-1 (qu)bits. We explain why the former circuit can be decomposed into 2w-1 control gates, whereas the latter circuit needs 2^w-1 control gates. We investigate whether computer circuits, not based on the full unitary group but instead on a subgroup of the unitary group, may be decomposable either into 2w-1 or into 2^w-1 control gates.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-1258500

- author
- De Vos, Alexis UGent and De Baerdemacker, Stijn UGent
- organization
- year
- 2011
- type
- journalArticle (original)
- publication status
- published
- subject
- keyword
- reversible computing, group theory, quantum computing
- journal title
- SYMMETRY-BASEL
- Symmetry-Basel
- volume
- 3
- issue
- 2
- issue title
- Symmetry in theoretical computer science
- pages
- 305 - 324
- Web of Science type
- Article
- Web of Science id
- 000208832200011
- ISSN
- 2073-8994
- DOI
- 10.3390/sym3020305
- language
- English
- UGent publication?
- yes
- classification
- A1
- copyright statement
*I have retained and own the full copyright for this publication*- id
- 1258500
- handle
- http://hdl.handle.net/1854/LU-1258500
- date created
- 2011-06-09 10:25:40
- date last changed
- 2016-12-19 15:38:09

@article{1258500, abstract = {Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e. the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with w bits and the decomposition of an arbitrary quantum circuit with w qubits. Both decompositions use the control gate as building block, i.e. a circuit transforming only one (qu)bit, the transformation being controlled by the other w-1 (qu)bits. We explain why the former circuit can be decomposed into 2w-1 control gates, whereas the latter circuit needs 2\^{ }w-1 control gates. We investigate whether computer circuits, not based on the full unitary group but instead on a subgroup of the unitary group, may be decomposable either into 2w-1 or into 2\^{ }w-1 control gates.}, author = {De Vos, Alexis and De Baerdemacker, Stijn}, issn = {2073-8994}, journal = {SYMMETRY-BASEL}, keyword = {reversible computing,group theory,quantum computing}, language = {eng}, number = {2}, pages = {305--324}, title = {Symmetry groups for the decomposition of reversible computers, quantum computers, and computers in between}, url = {http://dx.doi.org/10.3390/sym3020305}, volume = {3}, year = {2011}, }

- Chicago
- De Vos, Alexis, and Stijn De Baerdemacker. 2011. “Symmetry Groups for the Decomposition of Reversible Computers, Quantum Computers, and Computers in Between.”
*Symmetry-basel*3 (2): 305–324. - APA
- De Vos, Alexis, & De Baerdemacker, S. (2011). Symmetry groups for the decomposition of reversible computers, quantum computers, and computers in between.
*SYMMETRY-BASEL*,*3*(2), 305–324. - Vancouver
- 1.De Vos A, De Baerdemacker S. Symmetry groups for the decomposition of reversible computers, quantum computers, and computers in between. SYMMETRY-BASEL. 2011;3(2):305–24.
- MLA
- De Vos, Alexis, and Stijn De Baerdemacker. “Symmetry Groups for the Decomposition of Reversible Computers, Quantum Computers, and Computers in Between.”
*SYMMETRY-BASEL*3.2 (2011): 305–324. Print.