### Abstract

The Local Hamiltonian problem is the problem of estimating the least eigenvalue of a local Hamiltonian, and is complete for the class QMA. The 1D problem on a chain of qubits has heuristics which work well, while the 13-state qudit case has been shown to be QMA-complete. We show that this problem remains QMA-complete when the dimensionality of the qudits is brought down to 8.

Original language | English (US) |
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Pages (from-to) | 721-750 |

Number of pages | 30 |

Journal | Quantum Information and Computation |

Volume | 13 |

Issue number | 9-10 |

State | Published - Jul 23 2013 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Computational Theory and Mathematics

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## Cite this

Hallgren, S., Nagaj, D., & Narayanaswami, S. (2013). The local hamiltonian problem on a line with eight states is QMA-complete.

*Quantum Information and Computation*,*13*(9-10), 721-750.