Hardness of approximation for quantum problems
arXiv:1209.1055 · doi:10.1007/978-3-642-31594-7_33
Abstract
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 these 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.
21 pages, 1 figure, extended abstract appeared in Proceedings of the 39th International Colloquium on Automata, Languages and Programming (ICALP), pages 387-398, Springer, 2012
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Cited by in corpus (15)
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- The Complexity of Translationally Invariant Problems beyond Ground State Energies
- The 7 faces of quantum NP
- Finding resource states of measurement-based quantum computing is harder than quantum computing
- Approximation, Proof Systems, and Correlations in a Quantum World
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- Quantum State Isomorphism
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