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Title: Quantum algorithms and lower bounds for convex optimization
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.  more » « less
Award ID(s):
1816695
NSF-PAR ID:
10106373
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Quantum
Volume:
4
ISSN:
2521-327X
Page Range / eLocation ID:
221
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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