License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2013.80
URN: urn:nbn:de:0030-drops-43197
URL: https://drops.dagstuhl.de/opus/volltexte/2013/4319/
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Cosentino, Alessandro ; Kothari, Robin ; Paetznick, Adam

Dequantizing Read-once Quantum Formulas

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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.

BibTeX - Entry

@InProceedings{cosentino_et_al:LIPIcs:2013:4319,
  author =	{Alessandro Cosentino and Robin Kothari and Adam Paetznick},
  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 =	{Simone Severini and Fernando Brandao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4319},
  URN =		{urn:nbn:de:0030-drops-43197},
  doi =		{10.4230/LIPIcs.TQC.2013.80},
  annote =	{Keywords: formulas, dequantization, circuit complexity}
}

Keywords: formulas, dequantization, circuit complexity
Collection: 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)
Issue Date: 2013
Date of publication: 13.11.2013

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