### Abstract

*N*) qubits, where

*N*is the number of single-particle spin-orbitals, the CI matrix representation requires Õ(η

*)*qubits, where η ≪

*N*is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as Õ(η

^{2}

*N*

^{3}

*t*

Language | English |
---|---|

Article number | 015006 |

Pages | 1-37 |

Number of pages | 37 |

Journal | Quantum Science and Technology |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

### Fingerprint

### Bibliographical note

Copyright the Author(s) 2017. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.### Keywords

- quantum algorithm
- electronic structure
- quantum chemistry
- quantum simulation

### Cite this

*Quantum Science and Technology*,

*3*(1), 1-37. [015006]. https://doi.org/10.1088/2058-9565/aa9463

}

*Quantum Science and Technology*, vol. 3, no. 1, 015006, pp. 1-37. https://doi.org/10.1088/2058-9565/aa9463

**Exponentially more precise quantum simulation of fermions in the configuration interaction representation.** / Babbush, Ryan; Berry, Dominic W.; Sanders, Yuval R.; Kivlichan, Ian D.; Scherer, Artur; Wei, Annie Y.; Love, Peter J.; Aspuru-Guzik, Alán.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Exponentially more precise quantum simulation of fermions in the configuration interaction representation

AU - Babbush, Ryan

AU - Berry, Dominic W.

AU - Sanders, Yuval R.

AU - Kivlichan, Ian D.

AU - Scherer, Artur

AU - Wei, Annie Y.

AU - Love, Peter J.

AU - Aspuru-Guzik, Alán

N1 - Copyright the Author(s) 2017. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in Babbush et al (2016 New Journal of Physics 18, 033032), we employ a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper involves simulation under an oracle for the sparse, first-quantized representation of the molecular Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially more efficient than classical numerical methods. Whereas second-quantized representations of the wavefunction require Õ(N) qubits, where N is the number of single-particle spin-orbitals, the CI matrix representation requires Õ(η) qubits, where η ≪ N is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as Õ(η2N3t

AB - We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in Babbush et al (2016 New Journal of Physics 18, 033032), we employ a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper involves simulation under an oracle for the sparse, first-quantized representation of the molecular Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially more efficient than classical numerical methods. Whereas second-quantized representations of the wavefunction require Õ(N) qubits, where N is the number of single-particle spin-orbitals, the CI matrix representation requires Õ(η) qubits, where η ≪ N is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as Õ(η2N3t

KW - quantum algorithm

KW - electronic structure

KW - quantum chemistry

KW - quantum simulation

UR - http://purl.org/au-research/grants/arc/DP160102426

UR - http://www.scopus.com/inward/record.url?scp=85044303679&partnerID=8YFLogxK

U2 - 10.1088/2058-9565/aa9463

DO - 10.1088/2058-9565/aa9463

M3 - Article

VL - 3

SP - 1

EP - 37

JO - Quantum Science and Technology

T2 - Quantum Science and Technology

JF - Quantum Science and Technology

SN - 2058-9565

IS - 1

M1 - 015006

ER -