### Abstract

The model of adiabatic quantum computation is a relatively recent model of quantum computation that has attracted attention in the physics and computer science communities. We describe an efficient adiabatic simulation of any given quantum circuit. This implies that the adiabatic computation model and the standard circuit-based 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 one to state the main open problems in quantum computation using well-studied mathematical objects such as eigenvectors and spectral gaps of Hamiltonians.

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

Pages (from-to) | 755-787 |

Number of pages | 33 |

Journal | SIAM Review |

Volume | 50 |

Issue number | 4 |

DOIs | |

State | Published - 2008 |

### Fingerprint

### Keywords

- Adiabatic computation
- Nearest neighbor interactions
- Quantum computation

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Theoretical Computer Science

### Cite this

*SIAM Review*,

*50*(4), 755-787. https://doi.org/10.1137/080734479

**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 Review*, vol. 50, no. 4, pp. 755-787. https://doi.org/10.1137/080734479

}

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 - 2008

Y1 - 2008

N2 - The model of adiabatic quantum computation is a relatively recent model of quantum computation that has attracted attention in the physics and computer science communities. We describe an efficient adiabatic simulation of any given quantum circuit. This implies that the adiabatic computation model and the standard circuit-based 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 one to state the main open problems in quantum computation using well-studied mathematical objects such as eigenvectors and spectral gaps of Hamiltonians.

AB - The model of adiabatic quantum computation is a relatively recent model of quantum computation that has attracted attention in the physics and computer science communities. We describe an efficient adiabatic simulation of any given quantum circuit. This implies that the adiabatic computation model and the standard circuit-based 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 one to state the main open problems in quantum computation using well-studied mathematical objects such as eigenvectors and spectral gaps of Hamiltonians.

KW - Adiabatic computation

KW - Nearest neighbor interactions

KW - Quantum computation

UR - http://www.scopus.com/inward/record.url?scp=56349168935&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56349168935&partnerID=8YFLogxK

U2 - 10.1137/080734479

DO - 10.1137/080734479

M3 - Article

AN - SCOPUS:56349168935

VL - 50

SP - 755

EP - 787

JO - SIAM Review

JF - SIAM Review

SN - 0036-1445

IS - 4

ER -