Dequantizing Read-once Quantum Formulas
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.
formulas
dequantization
circuit complexity
80-92
Regular Paper
Alessandro
Cosentino
Alessandro Cosentino
Robin
Kothari
Robin Kothari
Adam
Paetznick
Adam Paetznick
10.4230/LIPIcs.TQC.2013.80
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode