%0 Journal Article %J Quantum %D 2020 %T Quantum algorithms and lower bounds for convex optimization %A Shouvanik Chakrabarti %A Andrew M. Childs %A Tongyang Li %A Xiaodi Wu %X

While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a convex function over an n-dimensional convex body using O~(n) queries to oracles that evaluate the objective function and determine membership in the convex body. This represents a quadratic improvement over the best-known classical algorithm. We also study limitations on the power of quantum computers for general convex optimization, showing that it requires Ω~(n−−√) evaluation queries and Ω(n−−√) membership queries.

%B Quantum %V 4 %8 12/18/2019 %G eng %U https://arxiv.org/abs/1809.01731 %N 221 %R https://doi.org/10.22331/q-2020-01-13-221