Improved techniques for preparing eigenstates of fermionic Hamiltonians

Dominic W. Berry, Mária Kieferová, Artur Scherer, Yuval R. Sanders, Guang Hao Low, Nathan Wiebe, Craig Gidney, Ryan Babbush

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. This is an exponential improvement over the previous state-of-the-art. Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure.
LanguageEnglish
Article number22
Pages1-7
Number of pages7
JournalNpj quantum information
Volume4
DOIs
Publication statusPublished - 2 May 2018

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eigenvectors
preparation
ground state
quantum chemistry
quantum computation
energy
chemical reactions
fermions
costs
excitation
simulation

Bibliographical note

Copyright The Author(s) 2018. 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.

Cite this

Berry, Dominic W. ; Kieferová, Mária ; Scherer, Artur ; Sanders, Yuval R. ; Low, Guang Hao ; Wiebe, Nathan ; Gidney, Craig ; Babbush, Ryan. / Improved techniques for preparing eigenstates of fermionic Hamiltonians. In: Npj quantum information. 2018 ; Vol. 4. pp. 1-7.
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abstract = "Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. This is an exponential improvement over the previous state-of-the-art. Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure.",
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Improved techniques for preparing eigenstates of fermionic Hamiltonians. / Berry, Dominic W.; Kieferová, Mária; Scherer, Artur; Sanders, Yuval R.; Low, Guang Hao; Wiebe, Nathan; Gidney, Craig; Babbush, Ryan.

In: Npj quantum information, Vol. 4, 22, 02.05.2018, p. 1-7.

Research output: Contribution to journalArticleResearchpeer-review

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