---
_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. <i>International Colloquium
    on Automata, Languages, and Programming (ICALP 2012)</i>. Springer Berlin Heidelberg;
    2012:387-398. doi:<a href="https://doi.org/10.1007/978-3-642-31594-7_33">10.1007/978-3-642-31594-7_33</a>'
  apa: Gharibian, S., &#38; Kempe, J. (2012). Hardness of Approximation for Quantum
    Problems. In A. Czumaj, K. Mehlhorn, A. Pitts, &#38; R. Wattenhofer (Eds.), <i>International
    Colloquium on Automata, Languages, and Programming (ICALP 2012)</i> (pp. 387–398).
    Springer Berlin Heidelberg. <a href="https://doi.org/10.1007/978-3-642-31594-7_33">https://doi.org/10.1007/978-3-642-31594-7_33</a>
  bibtex: '@inproceedings{Gharibian_Kempe_2012, place={Berlin, Heidelberg}, title={Hardness
    of Approximation for Quantum Problems}, DOI={<a href="https://doi.org/10.1007/978-3-642-31594-7_33">10.1007/978-3-642-31594-7_33</a>},
    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 <i>International Colloquium on Automata, Languages, and Programming
    (ICALP 2012)</i>, edited by Artur Czumaj, Kurt Mehlhorn, Andrew Pitts, and Roger
    Wattenhofer, 387–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. <a
    href="https://doi.org/10.1007/978-3-642-31594-7_33">https://doi.org/10.1007/978-3-642-31594-7_33</a>.'
  ieee: 'S. Gharibian and J. Kempe, “Hardness of Approximation for Quantum Problems,”
    in <i>International Colloquium on Automata, Languages, and Programming (ICALP
    2012)</i>, Warwick, UK, 2012, pp. 387–398, doi: <a href="https://doi.org/10.1007/978-3-642-31594-7_33">10.1007/978-3-642-31594-7_33</a>.'
  mla: Gharibian, Sevag, and Julia Kempe. “Hardness of Approximation for Quantum Problems.”
    <i>International Colloquium on Automata, Languages, and Programming (ICALP 2012)</i>,
    edited by Artur Czumaj et al., Springer Berlin Heidelberg, 2012, pp. 387–98, doi:<a
    href="https://doi.org/10.1007/978-3-642-31594-7_33">10.1007/978-3-642-31594-7_33</a>.
  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'
...