### Abstract

We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e., the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a polynomially increasing number of energy levels. A probe qubit is coupled to a quantum register that represents the system of interest such that the probe exhibits a dynamical response only when it is resonant with a transition in the system. By varying the probe's frequency and the system-probe coupling operator, any desired part of the energy spectrum can be obtained. The algorithm can also be used to deterministically prepare any energy eigenstate. As an example, we have simulated running the algorithm and obtained the energy spectrum of the water molecule.

Original language | English |
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Article number | 062304 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 85 |

Issue number | 6 |

DOIs | |

Publication status | Published - 5 Jun 2012 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*85*(6), [062304]. https://doi.org/10.1103/PhysRevA.85.062304

**Quantum algorithm for obtaining the energy spectrum of a physical system.** / Wang, Hefeng; Ashhab, Sahel; Nori, Franco.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 85, no. 6, 062304. https://doi.org/10.1103/PhysRevA.85.062304

}

TY - JOUR

T1 - Quantum algorithm for obtaining the energy spectrum of a physical system

AU - Wang, Hefeng

AU - Ashhab, Sahel

AU - Nori, Franco

PY - 2012/6/5

Y1 - 2012/6/5

N2 - We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e., the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a polynomially increasing number of energy levels. A probe qubit is coupled to a quantum register that represents the system of interest such that the probe exhibits a dynamical response only when it is resonant with a transition in the system. By varying the probe's frequency and the system-probe coupling operator, any desired part of the energy spectrum can be obtained. The algorithm can also be used to deterministically prepare any energy eigenstate. As an example, we have simulated running the algorithm and obtained the energy spectrum of the water molecule.

AB - We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e., the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a polynomially increasing number of energy levels. A probe qubit is coupled to a quantum register that represents the system of interest such that the probe exhibits a dynamical response only when it is resonant with a transition in the system. By varying the probe's frequency and the system-probe coupling operator, any desired part of the energy spectrum can be obtained. The algorithm can also be used to deterministically prepare any energy eigenstate. As an example, we have simulated running the algorithm and obtained the energy spectrum of the water molecule.

UR - http://www.scopus.com/inward/record.url?scp=84861879097&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861879097&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.85.062304

DO - 10.1103/PhysRevA.85.062304

M3 - Article

AN - SCOPUS:84861879097

VL - 85

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 6

M1 - 062304

ER -