Approximation algorithms for QMA-complete problems

Sevag Gharibian, Julia Kempe

Research output: Contribution to journalArticle

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 (where QMA stands for Quantum Merlin Arthur) and initiate its study. We present two main results. The first shows that a nontrivial 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, Karger, and Karpinski [J. Comput. System Sci., 58(1999), p. 193] to the quantum setting and might be of independent interest.

Original languageEnglish (US)
Pages (from-to)1028-1050
Number of pages23
JournalSIAM Journal on Computing
Volume41
Issue number4
DOIs
StatePublished - Sep 24 2012

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

Keywords

  • Approximation algorithm
  • Constraint satisfaction
  • Local Hamiltonian
  • QMA-complete

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

Cite this

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

In: SIAM Journal on Computing, Vol. 41, No. 4, 24.09.2012, p. 1028-1050.

Research output: Contribution to journalArticle

Gharibian, Sevag ; Kempe, Julia. / Approximation algorithms for QMA-complete problems. In: SIAM Journal on Computing. 2012 ; Vol. 41, No. 4. pp. 1028-1050.
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