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A Birkhoff connection between quantum circuits and linear classical reversible circuits

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Abstract
Birkhoff's theorem tells how any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. Similar theorems on unitary matrices reveal a connection between quantum circuits and linear classical reversible circuits. It triggers the question whether a quantum computer can be regarded as a superposition of classical reversible computers.
Keywords
Birkhoff's theorem, Unitary matrix, Permutation matrix, Quantum computation, Linear reversible computation, UNITARY MATRICES, THEOREM

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Citation

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MLA
De Vos, Alexis, and Stijn De Baerdemacker. “A Birkhoff Connection between Quantum Circuits and Linear Classical Reversible Circuits.” REVERSIBLE COMPUTATION (RC 2019), edited by Michael Kirkedal Thomsen and Mathias Soeken, vol. 11497, Springer, 2019, pp. 23–33.
APA
De Vos, A., & De Baerdemacker, S. (2019). A Birkhoff connection between quantum circuits and linear classical reversible circuits. In M. Kirkedal Thomsen & M. Soeken (Eds.), REVERSIBLE COMPUTATION (RC 2019) (Vol. 11497, pp. 23–33). Lausanne, Switzerland: Springer.
Chicago author-date
De Vos, Alexis, and Stijn De Baerdemacker. 2019. “A Birkhoff Connection between Quantum Circuits and Linear Classical Reversible Circuits.” In REVERSIBLE COMPUTATION (RC 2019), edited by Michael Kirkedal Thomsen and Mathias Soeken, 11497:23–33. Springer.
Chicago author-date (all authors)
De Vos, Alexis, and Stijn De Baerdemacker. 2019. “A Birkhoff Connection between Quantum Circuits and Linear Classical Reversible Circuits.” In REVERSIBLE COMPUTATION (RC 2019), ed by. Michael Kirkedal Thomsen and Mathias Soeken, 11497:23–33. Springer.
Vancouver
1.
De Vos A, De Baerdemacker S. A Birkhoff connection between quantum circuits and linear classical reversible circuits. In: Kirkedal Thomsen M, Soeken M, editors. REVERSIBLE COMPUTATION (RC 2019). Springer; 2019. p. 23–33.
IEEE
[1]
A. De Vos and S. De Baerdemacker, “A Birkhoff connection between quantum circuits and linear classical reversible circuits,” in REVERSIBLE COMPUTATION (RC 2019), Lausanne, Switzerland, 2019, vol. 11497, pp. 23–33.
@inproceedings{8621179,
  abstract     = {Birkhoff's theorem tells how any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. Similar theorems on unitary matrices reveal a connection between quantum circuits and linear classical reversible circuits. It triggers the question whether a quantum computer can be regarded as a superposition of classical reversible computers.},
  author       = {De Vos, Alexis and De Baerdemacker, Stijn},
  booktitle    = {REVERSIBLE COMPUTATION (RC 2019)},
  editor       = {Kirkedal Thomsen, Michael and Soeken, Mathias},
  isbn         = {9783030214999},
  issn         = {0302-9743},
  keywords     = {Birkhoff's theorem,Unitary matrix,Permutation matrix,Quantum computation,Linear reversible computation,UNITARY MATRICES,THEOREM},
  language     = {eng},
  location     = {Lausanne, Switzerland},
  pages        = {23--33},
  publisher    = {Springer},
  title        = {A Birkhoff connection between quantum circuits and linear classical reversible circuits},
  url          = {http://dx.doi.org/10.1007/978-3-030-21500-2_2},
  volume       = {11497},
  year         = {2019},
}

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