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The computational power of the square root of NOT

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Abstract
The quantum gates called`square root of NOT' and `controlled square root of NOT' can be applied to synthesize circuits, many more than all classical reversible circuits, but also many less than all quantum circuits. The circuits form an infinite but discrete group, i.e. a group with a countable infinity of elements. They are represented by unitary matrices. Classifying these matrices by `level' allows a detailed quantification of the computational power of the circuits.
Keywords
reversible computing, square root of NOT, quantum computing

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Citation

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Chicago
Vandenbrande, Steven, Raphaël Van Laer, and Alexis De Vos. 2012. “The Computational Power of the Square Root of NOT.” In 10th International Workshop on Boolean Problems, Proceedings, ed. Bernd Steinbach, 257–262. Freiberg, Germany: Bergakademie Freiberg.
APA
Vandenbrande, S., Van Laer, R., & De Vos, A. (2012). The computational power of the square root of NOT. In Bernd Steinbach (Ed.), 10th International Workshop on Boolean Problems, Proceedings (pp. 257–262). Presented at the 10th International Workshop on Boolean Problems, Freiberg, Germany: Bergakademie Freiberg.
Vancouver
1.
Vandenbrande S, Van Laer R, De Vos A. The computational power of the square root of NOT. In: Steinbach B, editor. 10th International Workshop on Boolean Problems, Proceedings. Freiberg, Germany: Bergakademie Freiberg; 2012. p. 257–62.
MLA
Vandenbrande, Steven, Raphaël Van Laer, and Alexis De Vos. “The Computational Power of the Square Root of NOT.” 10th International Workshop on Boolean Problems, Proceedings. Ed. Bernd Steinbach. Freiberg, Germany: Bergakademie Freiberg, 2012. 257–262. Print.
@inproceedings{2997670,
  abstract     = {The quantum gates called`square root of NOT' and `controlled square root of NOT' can be applied to synthesize circuits, many more than all classical reversible circuits, but also many less than all quantum circuits. The circuits form an infinite but discrete group, i.e. a group with a countable infinity of elements. They are represented by unitary matrices. Classifying these matrices by `level' allows a detailed quantification of the computational power of the circuits.},
  author       = {Vandenbrande, Steven and Van Laer, Rapha{\"e}l and De Vos, Alexis},
  booktitle    = {10th International Workshop on Boolean Problems, Proceedings},
  editor       = {Steinbach, Bernd},
  isbn         = {9783860124383},
  keyword      = {reversible computing,square root of NOT,quantum computing},
  language     = {eng},
  location     = {Freiberg, Germany},
  pages        = {257--262},
  publisher    = {Bergakademie Freiberg},
  title        = {The computational power of the square root of NOT},
  year         = {2012},
}