### Abstract

Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schrödinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multiconfigurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible. Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.

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

Pages (from-to) | 5388-5393 |

Number of pages | 6 |

Journal | Physical Chemistry Chemical Physics |

Volume | 10 |

Issue number | 35 |

DOIs | |

Publication status | Published - 8 Sep 2008 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Chemistry Chemical Physics*,

*10*(35), 5388-5393. https://doi.org/10.1039/b804804e

**Quantum algorithm for obtaining the energy spectrum of molecular systems.** / Wang, Hefeng; Kais, Sabre; Aspuru-Guzik, Alán; Hoffmann, Mark R.

Research output: Contribution to journal › Article

*Physical Chemistry Chemical Physics*, vol. 10, no. 35, pp. 5388-5393. https://doi.org/10.1039/b804804e

}

TY - JOUR

T1 - Quantum algorithm for obtaining the energy spectrum of molecular systems

AU - Wang, Hefeng

AU - Kais, Sabre

AU - Aspuru-Guzik, Alán

AU - Hoffmann, Mark R.

PY - 2008/9/8

Y1 - 2008/9/8

N2 - Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schrödinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multiconfigurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible. Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.

AB - Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schrödinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multiconfigurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible. Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.

UR - http://www.scopus.com/inward/record.url?scp=50849106399&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=50849106399&partnerID=8YFLogxK

U2 - 10.1039/b804804e

DO - 10.1039/b804804e

M3 - Article

VL - 10

SP - 5388

EP - 5393

JO - Physical Chemistry Chemical Physics

JF - Physical Chemistry Chemical Physics

SN - 1463-9076

IS - 35

ER -