article
Hardness of approximation for quantum problems
published
Sevag
Gharibian
author 715410000-0002-9992-3379
Julia
Kempe
author
623
department
7
department
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
eng
Hardness of approximationpolynomial time hierarchysuccinct set coverquantum complexity
Quantum Information & Computation
1209.1055
145-6517-540
yes
S. Gharibian, J. Kempe, Quantum Information & Computation 14 (2014) 517–540.
Gharibian S, Kempe J. Hardness of approximation for quantum problems. <i>Quantum Information & Computation</i>. 2014;14(5-6):517-540.
S. Gharibian and J. Kempe, “Hardness of approximation for quantum problems,” <i>Quantum Information & Computation</i>, vol. 14, no. 5–6, pp. 517–540, 2014.
Gharibian, Sevag, and Julia Kempe. “Hardness of Approximation for Quantum Problems.” <i>Quantum Information & Computation</i> 14, no. 5–6 (2014): 517–40.
Gharibian, S., & Kempe, J. (2014). Hardness of approximation for quantum problems. <i>Quantum Information & Computation</i>, <i>14</i>(5–6), 517–540.
Gharibian, Sevag, and Julia Kempe. “Hardness of Approximation for Quantum Problems.” <i>Quantum Information & Computation</i>, vol. 14, no. 5–6, 2014, pp. 517–40.
@article{Gharibian_Kempe_2014, title={Hardness of approximation for quantum problems}, volume={14}, number={5–6}, journal={Quantum Information & Computation}, author={Gharibian, Sevag and Kempe, Julia}, year={2014}, pages={517–540} }
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