### 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 language | English (US) |
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Title of host publication | Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011 |

Pages | 178-188 |

Number of pages | 11 |

DOIs | |

State | Published - Aug 29 2011 |

Event | 26th Annual IEEE Conference on Computational Complexity, CCC 2011 - San Jose, CA, United States Duration: Jun 8 2011 → Jun 10 2011 |

### Other

Other | 26th Annual IEEE Conference on Computational Complexity, CCC 2011 |
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Country | United States |

City | San Jose, CA |

Period | 6/8/11 → 6/10/11 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- Computational Mathematics

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Approximation algorithms for QMA-complete problems

AU - Gharibian, Sevag

AU - Kempe, Julia

PY - 2011/8/29

Y1 - 2011/8/29

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Exhaustive sampling

KW - Local Hamiltonian

KW - QMA-complete

UR - http://www.scopus.com/inward/record.url?scp=80052014767&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052014767&partnerID=8YFLogxK

U2 - 10.1109/CCC.2011.15

DO - 10.1109/CCC.2011.15

M3 - Conference contribution

SN - 9780769544113

SP - 178

EP - 188

BT - Proceedings - 26th Annual IEEE Conference on Computational Complexity, CCC 2011

ER -