### Abstract

Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models allows stating the main open problems in quantum computation using well-studied mathematical objects such as eigenvectors and spectral gaps of sparse matrices.

Original language | English (US) |
---|---|

Pages (from-to) | 166-194 |

Number of pages | 29 |

Journal | SIAM Journal on Computing |

Volume | 37 |

Issue number | 1 |

DOIs | |

State | Published - 2007 |

### Fingerprint

### Keywords

- Adiabatic computation
- Nearest neighbor interactions
- Quantum computation

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Computing*,

*37*(1), 166-194. https://doi.org/10.1137/S0097539705447323

**Adiabatic quantum computation is equivalent to standard quantum computation.** / Aharonov, Dorit; Van Dam, Wim; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded.

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 37, no. 1, pp. 166-194. https://doi.org/10.1137/S0097539705447323

}

TY - JOUR

T1 - Adiabatic quantum computation is equivalent to standard quantum computation

AU - Aharonov, Dorit

AU - Van Dam, Wim

AU - Kempe, Julia

AU - Landau, Zeph

AU - Lloyd, Seth

AU - Regev, Oded

PY - 2007

Y1 - 2007

N2 - Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models allows stating the main open problems in quantum computation using well-studied mathematical objects such as eigenvectors and spectral gaps of sparse matrices.

AB - Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models allows stating the main open problems in quantum computation using well-studied mathematical objects such as eigenvectors and spectral gaps of sparse matrices.

KW - Adiabatic computation

KW - Nearest neighbor interactions

KW - Quantum computation

UR - http://www.scopus.com/inward/record.url?scp=38349169118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38349169118&partnerID=8YFLogxK

U2 - 10.1137/S0097539705447323

DO - 10.1137/S0097539705447323

M3 - Article

AN - SCOPUS:38349169118

VL - 37

SP - 166

EP - 194

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 1

ER -