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arXiv · 1304.5164

Dequantizing read-once quantum formulas

Alessandro Cosentino·Robin Kothari·Adam Paetznick
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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.

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Alessandro Cosentino, Robin Kothari, Adam Paetznick. 2013-04-18. Dequantizing read-once quantum formulas. https://doi.org/10.4230/lipics.tqc.2013.80

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