|Title||Quantum algorithms and lower bounds for convex optimization|
|Publication Type||Journal Article|
|Year of Publication||2018|
|Authors||Chakrabarti, S, Childs, AM, Li, T, 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.