Dequantizing Read-once Quantum Formulas

Cosentino, Alessandro; Kothari, Robin; Paetznick, Adam

doi:10.4230/LIPIcs.TQC.2013.80

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Dequantizing Read-once Quantum Formulas

Authors Alessandro Cosentino, Robin Kothari, Adam Paetznick

Part of: Volume: 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2013-11-13

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Document Identifiers

DOI: 10.4230/LIPIcs.TQC.2013.80
URN: urn:nbn:de:0030-drops-43197

Subject Classification

Keywords

formulas
dequantization
circuit complexity

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.TQC.2013.80

Author Details

Alessandro Cosentino

Robin Kothari

Adam Paetznick

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