Approximation algorithms for QMA-complete problems

Sevag Gharibian, Julia Kempe

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and initiate its study. We present two main results. The first shows that a non-trivial approximation ratio can be obtained in the class NP using product states. The second result (which builds on the first one), gives a polynomial time (classical) algorithm providing a similar approximation ratio for dense instances of the problem. The latter result is based on an adaptation of the "exhaustive sampling method" by Arora et al. [J. Comp. Sys. Sci. 58, p. 193 (1999)] to the quantum setting, and might be of independent interest.

Original languageEnglish (US)
Title of host publicationProceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011
Pages178-188
Number of pages11
DOIs
StatePublished - Aug 29 2011
Event26th Annual IEEE Conference on Computational Complexity, CCC 2011 - San Jose, CA, United States
Duration: Jun 8 2011Jun 10 2011

Other

Other26th Annual IEEE Conference on Computational Complexity, CCC 2011
CountryUnited States
CitySan Jose, CA
Period6/8/116/10/11

Fingerprint

Hamiltonians
Constraint satisfaction problems
Approximation algorithms
Computer science
Approximation Algorithms
Polynomials
Sampling
Approximation
Constraint Satisfaction Problem
Sampling Methods
Polynomial time
Computer Science

Keywords

  • Approximation algorithms
  • Exhaustive sampling
  • Local Hamiltonian
  • QMA-complete

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Computational Mathematics

Cite this

Gharibian, S., & Kempe, J. (2011). Approximation algorithms for QMA-complete problems. In Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011 (pp. 178-188). [5959807] https://doi.org/10.1109/CCC.2011.15

Approximation algorithms for QMA-complete problems. / Gharibian, Sevag; Kempe, Julia.

Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011. 2011. p. 178-188 5959807.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Gharibian, S & Kempe, J 2011, Approximation algorithms for QMA-complete problems. in Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011., 5959807, pp. 178-188, 26th Annual IEEE Conference on Computational Complexity, CCC 2011, San Jose, CA, United States, 6/8/11. https://doi.org/10.1109/CCC.2011.15
Gharibian S, Kempe J. Approximation algorithms for QMA-complete problems. In Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011. 2011. p. 178-188. 5959807 https://doi.org/10.1109/CCC.2011.15
Gharibian, Sevag ; Kempe, Julia. / Approximation algorithms for QMA-complete problems. Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011. 2011. pp. 178-188
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