Advanced search
1 file | 206.56 KB

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

Alexis De Vos (UGent) and Stijn De Baerdemacker (UGent)
(2011) SYMMETRY-BASEL. 3(2). p.305-324
Author
Organization
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.
Keywords
reversible computing, group theory, quantum computing

Downloads

  • symmetry-03-00305.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 206.56 KB

Citation

Please use this url to cite or link to this publication:

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.
@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},
}

Altmetric
View in Altmetric
Web of Science
Times cited: