TY - JOUR
AB - 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.
AU - Gharibian, Sevag
AU - Kempe, Julia
ID - 8171
IS - 5-6
JF - Quantum Information & Computation
KW - Hardness of approximation
KW - polynomial time hierarchy
KW - succinct set cover
KW - quantum complexity
TI - Hardness of approximation for quantum problems
VL - 14
ER -