Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations

Eric J. Bylaska; Duo Song; Nicholas P. Bauman; Karol Kowalski; Daniel Claudino; Travis S. Humble

doi:10.3389/fchem.2021.603019

Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations

Eric J. Bylaska, Duo Song, Nicholas P. Bauman, Karol Kowalski, Daniel Claudino, Travis S. Humble

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

8 Scopus citations

Abstract

For many-body methods such as MCSCF and CASSCF, in which the number of one-electron orbitals is optimized and independent of the basis set used, there are no problems with using plane-wave basis sets. However, for methods currently used in quantum computing such as select configuration interaction (CI) and coupled cluster (CC) methods, it is necessary to have a virtual space that is able to capture a significant amount of electron-electron correlation in the system. The virtual orbitals in a pseudopotential plane-wave Hartree–Fock calculation, because of Coulomb repulsion, are often scattering states that interact very weakly with the filled orbitals. As a result, very little correlation energy is captured from them. The use of virtual spaces derived from the one-electron operators has also been tried, and while some correlations are captured, the amount is quite low. To overcome these limitations, we have been developing new classes of algorithms to define virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. With these procedures, we have been able to derive virtual spaces, containing only a few orbitals, which are able to capture a significant amount of correlation. The focus in this manuscript is on using these derived basis sets to target full CI (FCI) quality results for H₂ on near-term quantum computers. However, the initial results for this approach were promising. We were able to obtain good agreement with FCI/cc-pVTZ results for this system with just 4 virtual orbitals, using both FCI and quantum simulations. The quality of the results using COVOs suggests that it may be possible to use them in other many-body approaches, including coupled cluster and Møller–Plesset perturbation theories, and open up the door to many-body calculations for pseudopotential plane-wave basis set methods.

Original language	English
Article number	603019
Journal	Frontiers in Chemistry
Volume	9
DOIs	https://doi.org/10.3389/fchem.2021.603019
State	Published - Mar 18 2021

Funding

We would like to thank the NWChem project team and the people that have helped the progress of the NWChem software over the years. DC would like to thank Alexander McCaskey for discussions and help with the software engineering of the quantum algorithm used in this paper. This material is based upon work supported by the United States Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division through its “Embedding Quantum Computing into Many-body Frameworks for Strongly Correlated Molecular and Materials Systems” project at Pacific Northwest National Laboratory (PNNL). This work was also supported by the Quantum Science Center (QSC), a National Quantum Information Science Research Center of the United States Department of Energy (DOE). We also would like to thank the DOE BES Chem CCS, DOE BES Geochemistry, and DOE Advanced Scientific Computing Research (ASCR) ECP NWChemEx programs for their support of software development for high-performance computers and computer time needed to carry out the work. PNNL is operated for the United States Department of Energy by the Battelle Memorial Institute under Contract DE-AC06-76RLO-1830. This research was also partially supported, thru their support of software development for high-performance computers, by DOE BES Chem CCS and DOE BES Geosciences programs, as well as the Exascale Computing Project (17-SC-20-SC), a collaborative effort

Funders	Funder number
NWChem project team
National Quantum Information Science Research Center
Quantum Science Center
U.S. Department of Energy
Battelle	DE-AC06-76RLO-1830
Office of Science
Basic Energy Sciences	17-SC-20-SC
Pacific Northwest National Laboratory
Chemical Sciences, Geosciences, and Biosciences Division

Keywords

ADAPT-VQE
COVOs
DUCC
correlation optimized virtual orbitals
many-body calculations
nwchem
pseudopotential plane-wave
quantum computing

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10.3389/fchem.2021.603019

Cite this

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title = "Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations",

abstract = "For many-body methods such as MCSCF and CASSCF, in which the number of one-electron orbitals is optimized and independent of the basis set used, there are no problems with using plane-wave basis sets. However, for methods currently used in quantum computing such as select configuration interaction (CI) and coupled cluster (CC) methods, it is necessary to have a virtual space that is able to capture a significant amount of electron-electron correlation in the system. The virtual orbitals in a pseudopotential plane-wave Hartree–Fock calculation, because of Coulomb repulsion, are often scattering states that interact very weakly with the filled orbitals. As a result, very little correlation energy is captured from them. The use of virtual spaces derived from the one-electron operators has also been tried, and while some correlations are captured, the amount is quite low. To overcome these limitations, we have been developing new classes of algorithms to define virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. With these procedures, we have been able to derive virtual spaces, containing only a few orbitals, which are able to capture a significant amount of correlation. The focus in this manuscript is on using these derived basis sets to target full CI (FCI) quality results for H2 on near-term quantum computers. However, the initial results for this approach were promising. We were able to obtain good agreement with FCI/cc-pVTZ results for this system with just 4 virtual orbitals, using both FCI and quantum simulations. The quality of the results using COVOs suggests that it may be possible to use them in other many-body approaches, including coupled cluster and M{\o}ller–Plesset perturbation theories, and open up the door to many-body calculations for pseudopotential plane-wave basis set methods.",

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author = "Bylaska, {Eric J.} and Duo Song and Bauman, {Nicholas P.} and Karol Kowalski and Daniel Claudino and Humble, {Travis S.}",

note = "Publisher Copyright: {\textcopyright} Copyright {\textcopyright} 2021 Bylaska, Song, Bauman, Kowalski, Claudino and Humble.",

year = "2021",

month = mar,

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doi = "10.3389/fchem.2021.603019",

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T2 - Abridging Virtual Spaces Through the Optimization of Pairwise Correlations

AU - Bylaska, Eric J.

AU - Song, Duo

AU - Bauman, Nicholas P.

AU - Kowalski, Karol

AU - Claudino, Daniel

AU - Humble, Travis S.

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Y1 - 2021/3/18

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AB - For many-body methods such as MCSCF and CASSCF, in which the number of one-electron orbitals is optimized and independent of the basis set used, there are no problems with using plane-wave basis sets. However, for methods currently used in quantum computing such as select configuration interaction (CI) and coupled cluster (CC) methods, it is necessary to have a virtual space that is able to capture a significant amount of electron-electron correlation in the system. The virtual orbitals in a pseudopotential plane-wave Hartree–Fock calculation, because of Coulomb repulsion, are often scattering states that interact very weakly with the filled orbitals. As a result, very little correlation energy is captured from them. The use of virtual spaces derived from the one-electron operators has also been tried, and while some correlations are captured, the amount is quite low. To overcome these limitations, we have been developing new classes of algorithms to define virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. With these procedures, we have been able to derive virtual spaces, containing only a few orbitals, which are able to capture a significant amount of correlation. The focus in this manuscript is on using these derived basis sets to target full CI (FCI) quality results for H2 on near-term quantum computers. However, the initial results for this approach were promising. We were able to obtain good agreement with FCI/cc-pVTZ results for this system with just 4 virtual orbitals, using both FCI and quantum simulations. The quality of the results using COVOs suggests that it may be possible to use them in other many-body approaches, including coupled cluster and Møller–Plesset perturbation theories, and open up the door to many-body calculations for pseudopotential plane-wave basis set methods.

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Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations

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