@article{Brando2013ExponentialQS,
title={Exponential quantum speed-ups are generic},
author={Fernando G. S. L. Brand{\~a}o and Michal Horodecki},
journal={Quantum Information & Computation},
year={2013},
volume={13},
pages={901-924}
}

Published 2013 in Quantum Information & Computation

A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any sufficiently long quantum circuit one can construct a black-box problem which is solved by the circuit with a constant number of quantum queries, but which requires exponentially many classical queries, even if the classical machine has the ability to postselect.