# Possibilistic simulation of quantum circuits by classical circuits

@article{Wang2019PossibilisticSO,
title={Possibilistic simulation of quantum circuits by classical circuits},
author={Daochen Wang},
journal={Physical Review A},
year={2019}
}
• Daochen Wang
• Published 10 April 2019
• Computer Science
• Physical Review A
In a recent breakthrough, Bravyi, Gosset and Konig (BGK) [Science, 2018] proved that a family of shallow quantum circuits cannot be simulated by shallow classical circuits. In our paper, we first formalise their notion of simulation, which we call possibilistic simulation. We then construct classical circuits, using {NOT, AND, OR} gates of fan-in $\leq 2$, that can simulate any given quantum circuit with Clifford+$T$ gates. Our constructions give log-depth classical circuits that solve the…

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It is shown that even for single-qubit Cliﬀord-gate-teleportation circuits this simulation problem cannot be solved by constant-depth classical circuits with bounded fan-in gates, and a reduction to the problem of computing the parity is obtained, a well-studied problem in classical circuit complexity.

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