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Block-ZXZ synthesis of an arbitrary quantum circuit

Alexis De Vos (UGent) and Stijn De Baerdemacker (UGent)
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Abstract
Given an arbitrary 2(w) x 2(w) unitary matrix U, a powerful matrix decomposition can be applied, leading to four different syntheses of a w-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by H. Fuhr and Z. Rzeszotnik [Linear Algebra Its Appl. 484, 86 (2015)] generalizing the scaling of single-bit unitary gates (w = 1) to gates with arbitrary value of w. The synthesized circuit consists of controlled one-qubit gates, such as NEGATOR gates and PHASOR gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled NOT gates in the case that U is a permutation matrix.
Keywords
quantum computing, unitary matrix

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Citation

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

Chicago
De Vos, Alexis, and Stijn De Baerdemacker. 2016. “Block-ZXZ Synthesis of an Arbitrary Quantum Circuit.” Physical Review A 94 (5).
APA
De Vos, Alexis, & De Baerdemacker, S. (2016). Block-ZXZ synthesis of an arbitrary quantum circuit. PHYSICAL REVIEW A, 94(5).
Vancouver
1.
De Vos A, De Baerdemacker S. Block-ZXZ synthesis of an arbitrary quantum circuit. PHYSICAL REVIEW A. 2016;94(5).
MLA
De Vos, Alexis, and Stijn De Baerdemacker. “Block-ZXZ Synthesis of an Arbitrary Quantum Circuit.” PHYSICAL REVIEW A 94.5 (2016): n. pag. Print.
@article{8199072,
  abstract     = {Given an arbitrary 2(w) x 2(w) unitary matrix U, a powerful matrix decomposition can be applied, leading to four different syntheses of a w-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by H. Fuhr and Z. Rzeszotnik [Linear Algebra Its Appl. 484, 86 (2015)] generalizing the scaling of single-bit unitary gates (w = 1) to gates with arbitrary value of w. The synthesized circuit consists of controlled one-qubit gates, such as NEGATOR gates and PHASOR gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled NOT gates in the case that U is a permutation matrix.},
  articleno    = {052317},
  author       = {De Vos, Alexis and De Baerdemacker, Stijn},
  issn         = {2469-9926},
  journal      = {PHYSICAL REVIEW A},
  language     = {eng},
  number       = {5},
  pages        = {7},
  title        = {Block-ZXZ synthesis of an arbitrary quantum circuit},
  volume       = {94},
  year         = {2016},
}

Web of Science
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