### 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) |
---|---|

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 |

### Fingerprint

### 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

### Cite this

*Quantum Information and Computation*,

*13*(9-10), 721-750.

}

*Quantum Information and Computation*, vol. 13, no. 9-10, pp. 721-750.

**The local hamiltonian problem on a line with eight states is QMA-complete.** / Hallgren, Sean; Nagaj, Daniel; Narayanaswami, Sandeep.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The local hamiltonian problem on a line with eight states is QMA-complete

AU - Hallgren, Sean

AU - Nagaj, Daniel

AU - Narayanaswami, Sandeep

PY - 2013/7/23

Y1 - 2013/7/23

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84880254341&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880254341&partnerID=8YFLogxK

M3 - Article

VL - 13

SP - 721

EP - 750

JO - Quantum Information and Computation

JF - Quantum Information and Computation

SN - 1533-7146

IS - 9-10

ER -