---
_id: '8169'
abstract:
- lang: eng
text: 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.
Our work thus yields the first known hardness of approximation results for a quantum
complexity class. 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 1999). We close by showing
that a variant of the local Hamiltonian problem with hybrid classical-quantum
ground states is complete for the second level of our quantum hierarchy.
author:
- first_name: Sevag
full_name: Gharibian, Sevag
id: '71541'
last_name: Gharibian
orcid: 0000-0002-9992-3379
- first_name: Julia
full_name: Kempe, Julia
last_name: Kempe
citation:
ama: 'Gharibian S, Kempe J. Hardness of Approximation for Quantum Problems. In:
Czumaj A, Mehlhorn K, Pitts A, Wattenhofer R, eds. International Colloquium
on Automata, Languages, and Programming (ICALP 2012). Springer Berlin Heidelberg;
2012:387-398. doi:10.1007/978-3-642-31594-7_33'
apa: Gharibian, S., & Kempe, J. (2012). Hardness of Approximation for Quantum
Problems. In A. Czumaj, K. Mehlhorn, A. Pitts, & R. Wattenhofer (Eds.), International
Colloquium on Automata, Languages, and Programming (ICALP 2012) (pp. 387–398).
Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_33
bibtex: '@inproceedings{Gharibian_Kempe_2012, place={Berlin, Heidelberg}, title={Hardness
of Approximation for Quantum Problems}, DOI={10.1007/978-3-642-31594-7_33},
booktitle={International Colloquium on Automata, Languages, and Programming (ICALP
2012)}, publisher={Springer Berlin Heidelberg}, author={Gharibian, Sevag and Kempe,
Julia}, editor={Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew and Wattenhofer,
Roger}, year={2012}, pages={387–398} }'
chicago: 'Gharibian, Sevag, and Julia Kempe. “Hardness of Approximation for Quantum
Problems.” In International Colloquium on Automata, Languages, and Programming
(ICALP 2012), edited by Artur Czumaj, Kurt Mehlhorn, Andrew Pitts, and Roger
Wattenhofer, 387–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. https://doi.org/10.1007/978-3-642-31594-7_33.'
ieee: 'S. Gharibian and J. Kempe, “Hardness of Approximation for Quantum Problems,”
in International Colloquium on Automata, Languages, and Programming (ICALP
2012), Warwick, UK, 2012, pp. 387–398, doi: 10.1007/978-3-642-31594-7_33.'
mla: Gharibian, Sevag, and Julia Kempe. “Hardness of Approximation for Quantum Problems.”
International Colloquium on Automata, Languages, and Programming (ICALP 2012),
edited by Artur Czumaj et al., Springer Berlin Heidelberg, 2012, pp. 387–98, doi:10.1007/978-3-642-31594-7_33.
short: 'S. Gharibian, J. Kempe, in: A. Czumaj, K. Mehlhorn, A. Pitts, R. Wattenhofer
(Eds.), International Colloquium on Automata, Languages, and Programming (ICALP
2012), Springer Berlin Heidelberg, Berlin, Heidelberg, 2012, pp. 387–398.'
conference:
location: Warwick, UK
name: International Colloquium on Automata, Languages, and Programming (ICALP)
date_created: 2019-03-01T11:55:18Z
date_updated: 2023-02-28T11:03:26Z
department:
- _id: '623'
- _id: '7'
doi: 10.1007/978-3-642-31594-7_33
editor:
- first_name: Artur
full_name: Czumaj, Artur
last_name: Czumaj
- first_name: Kurt
full_name: Mehlhorn, Kurt
last_name: Mehlhorn
- first_name: Andrew
full_name: Pitts, Andrew
last_name: Pitts
- first_name: Roger
full_name: Wattenhofer, Roger
last_name: Wattenhofer
extern: '1'
external_id:
arxiv:
- '1209.1055'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1209.1055
oa: '1'
page: 387-398
place: Berlin, Heidelberg
publication: International Colloquium on Automata, Languages, and Programming (ICALP
2012)
publication_identifier:
isbn:
- 978-3-642-31594-7
publication_status: published
publisher: Springer Berlin Heidelberg
status: public
title: Hardness of Approximation for Quantum Problems
type: conference
user_id: '71541'
year: '2012'
...