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

Ryan Babbush, Dominic W. Berry, Yuval R. Sanders, Ian D. Kivlichan, Artur Scherer, Annie Y. Wei, Peter J. Love, Alán Aspuru-Guzik

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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
LanguageEnglish
Article number015006
Pages1-37
Number of pages37
JournalQuantum Science and Technology
Volume3
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

Fingerprint

Fermions
configuration interaction
fermions
Hamiltonians
matrices
simulation
particle spin
Taylor series
Wave functions
Numerical methods
Physics
scaling
orbitals
physics
Molecules
Electrons
molecules
electrons

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

Babbush, Ryan ; Berry, Dominic W. ; Sanders, Yuval R. ; Kivlichan, Ian D. ; Scherer, Artur ; Wei, Annie Y. ; Love, Peter J. ; Aspuru-Guzik, Alán. / Exponentially more precise quantum simulation of fermions in the configuration interaction representation. In: Quantum Science and Technology. 2018 ; Vol. 3, No. 1. pp. 1-37.
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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.

In: Quantum Science and Technology, Vol. 3, No. 1, 015006, 01.01.2018, p. 1-37.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Wei, Annie Y.

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