Affiliation:
1. QuSoft, CWI, Amsterdam, the Netherlands
2. QuSoft, CWI and University of Amsterdam, the Netherlands
Abstract
Brandão and Svore \cite{brandao2016QSDPSpeedup} recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension n of the problem and the number m of constraints, but worse in terms of various other parameters. In this paper we improve their algorithms in several ways, getting better dependence on those other parameters. To this end we develop new techniques for quantum algorithms, for instance a general way to efficiently implement smooth functions of sparse Hamiltonians, and a generalized minimum-finding procedure.We also show limits on this approach to quantum SDP-solvers, for instance for combinatorial optimization problems that have a lot of symmetry. Finally, we prove some general lower bounds showing that in the worst case, the complexity of every quantum LP-solver (and hence also SDP-solver) has to scale linearly with mn when m≈n, which is the same as classical.
Publisher
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Subject
Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics
Cited by
44 articles.
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