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DOI: 10.4230/LIPIcs.TQC.2013.80
Dequantizing Read-once Quantum Formulas

Authors: Alessandro Cosentino, Robin Kothari, and Adam Paetznick

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

Abstract
Quantum formulas, defined by Yao [FOCS'93], are the quantum analogs of classical formulas, i.e., classical circuits in which all gates have fanout one. We show that any read-once quantum formula over a gate set that contains all single-qubit gates is equivalent to a read-once classical formula of the same size and depth over an analogous classical gate set. For example, any read-once quantum formula over Toffoli and single-qubit gates is equivalent to a read-once classical formula over Toffoli and NOT gates. We then show that the equivalence does not hold if the read-once restriction is removed. To show the power of quantum formulas without the read-once restriction, we define a new model of computation called the one-qubit model and show that it can compute all boolean functions. This model may also be of independent interest.
Cite as

Alessandro Cosentino, Robin Kothari, and Adam Paetznick. Dequantizing Read-once Quantum Formulas. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 80-92, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{cosentino_et_al:LIPIcs.TQC.2013.80,
  author =	{Cosentino, Alessandro and Kothari, Robin and Paetznick, Adam},
  title =	{{Dequantizing Read-once Quantum Formulas}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{80--92},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.80},
  URN =		{urn:nbn:de:0030-drops-43197},
  doi =		{10.4230/LIPIcs.TQC.2013.80},
  annote =	{Keywords: formulas, dequantization, circuit complexity}
}
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