LIPIcs.TQC.2013.80.pdf
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Dequantizing Read-once Quantum Formulas
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8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
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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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
https://doi.org/10.4230/LIPIcs.TQC.2013.80
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.
Keywords
- formulas
- dequantization
- circuit complexity
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