Hardness of approximation for quantum problems
Gharibian, Sevag
Kempe, Julia
Hardness of approximation
polynomial time hierarchy
succinct set cover
quantum complexity
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define
a quantum generalization of the polynomial hierarchy, and initiate its study. We show that
not only are there natural complete problems for the second level of this quantum hierarchy, but that these problems are in fact hard to approximate. Using the same techniques, we
also obtain hardness of approximation for the class QCMA. Our approach is based on the
use of dispersers, and is inspired by the classical results of Umans regarding hardness of approximation for the second level of the classical polynomial hierarchy [Umans, FOCS 1999].
The problems for which we prove hardness of approximation for include, among others, a
quantum version of the Succinct Set Cover problem, and a variant of the local Hamiltonian
problem with hybrid classical-quantum ground states.
2014
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://ris.uni-paderborn.de/record/8171
Gharibian S, Kempe J. Hardness of approximation for quantum problems. <i>Quantum Information & Computation</i>. 2014;14(5-6):517-540.
eng
info:eu-repo/semantics/altIdentifier/arxiv/1209.1055
info:eu-repo/semantics/openAccess