### Abstract

Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.

Original language | English |
---|---|

Article number | 144112 |

Journal | Journal of Chemical Physics |

Volume | 134 |

Issue number | 14 |

DOIs | |

Publication status | Published - 14 Apr 2011 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

**Decomposition of unitary matrices for finding quantum circuits : Application to molecular Hamiltonians.** / Daskin, Anmer; Kais, Sabre.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 134, no. 14, 144112. https://doi.org/10.1063/1.3575402

}

TY - JOUR

T1 - Decomposition of unitary matrices for finding quantum circuits

T2 - Application to molecular Hamiltonians

AU - Daskin, Anmer

AU - Kais, Sabre

PY - 2011/4/14

Y1 - 2011/4/14

N2 - Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.

AB - Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.

UR - http://www.scopus.com/inward/record.url?scp=79954579639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79954579639&partnerID=8YFLogxK

U2 - 10.1063/1.3575402

DO - 10.1063/1.3575402

M3 - Article

C2 - 21495747

AN - SCOPUS:79954579639

VL - 134

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 14

M1 - 144112

ER -