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Title: Quantum-classical hybrid algorithm for the simulation of all-electron correlation

Abstract

While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. Furthermore, we obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of themore » developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
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  1. Univ. of Chicago, IL (United States)
Publication Date:
Research Org.:
Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1871654
Alternate Identifier(s):
OSTI ID: 1837608
Grant/Contract Number:  
SC0019215; SC002183
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 155; Journal Issue: 24; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Quantum computing; Schrodinger equations; Statistical analysis; Electronic correlation; Density matrix method; Quantum algorithms; Complete-active space self-consistent field; Isomerism; Correlation energy; Density functional theory

Citation Formats

Boyn, Jan-Niklas, Lykhin, Aleksandr O., Smart, Scott E., Gagliardi, Laura, and Mazziotti, David A. Quantum-classical hybrid algorithm for the simulation of all-electron correlation. United States: N. p., 2021. Web. doi:10.1063/5.0074842.
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Boyn, Jan-Niklas, Lykhin, Aleksandr O., Smart, Scott E., Gagliardi, Laura, & Mazziotti, David A. Quantum-classical hybrid algorithm for the simulation of all-electron correlation. United States. https://doi.org/10.1063/5.0074842
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Boyn, Jan-Niklas, Lykhin, Aleksandr O., Smart, Scott E., Gagliardi, Laura, and Mazziotti, David A. Tue . "Quantum-classical hybrid algorithm for the simulation of all-electron correlation". United States. https://doi.org/10.1063/5.0074842. https://www.osti.gov/servlets/purl/1871654.
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@article{osti_1871654,
title = {Quantum-classical hybrid algorithm for the simulation of all-electron correlation},
author = {Boyn, Jan-Niklas and Lykhin, Aleksandr O. and Smart, Scott E. and Gagliardi, Laura and Mazziotti, David A.},
abstractNote = {While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. Furthermore, we obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of the developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.},
doi = {10.1063/5.0074842},
journal = {Journal of Chemical Physics},
number = 24,
volume = 155,
place = {United States},
year = {Tue Dec 28 00:00:00 EST 2021},
month = {Tue Dec 28 00:00:00 EST 2021}
}
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https://doi.org/10.1063/5.0074842
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Works referenced in this record:

Sub-system quantum dynamics using coupled cluster downfolding techniques
journal, June 2020

  • Kowalski, Karol; Bauman, Nicholas P.
  • The Journal of Chemical Physics, Vol. 152, Issue 24
  • DOI: 10.1063/5.0008436

P y SCF: the Python-based simulations of chemistry framework : The PySCF program
journal, September 2017

  • Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1
  • DOI: 10.1002/wcms.1340

Approximating q -order reduced density matrices in terms of the lower-order ones. I. General relations
journal, February 1993

  • Colmenero, F.; Pérez del Valle, C.; Valdemoro, C.
  • Physical Review A, Vol. 47, Issue 2
  • DOI: 10.1103/physreva.47.971

Combining Pair-Density Functional Theory and Variational Two-Electron Reduced-Density Matrix Methods
journal, November 2018

  • Mostafanejad, Mohammad; DePrince, A. Eugene
  • Journal of Chemical Theory and Computation, Vol. 15, Issue 1
  • DOI: 10.1021/acs.jctc.8b00988

Excited-State Spectra of Strongly Correlated Molecules from a Reduced-Density-Matrix Approach
journal, September 2018

  • Hemmatiyan, S.; Sajjan, M.; Schlimgen, A. W.
  • The Journal of Physical Chemistry Letters, Vol. 9, Issue 18
  • DOI: 10.1021/acs.jpclett.8b02455

Towards a formal definition of static and dynamic electronic correlations
journal, January 2017

  • Benavides-Riveros, Carlos L.; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
  • Physical Chemistry Chemical Physics, Vol. 19, Issue 20
  • DOI: 10.1039/c7cp01137g

Multiconfiguration pair-density functional theory investigation of the electronic spectrum of MnO 4 −
journal, March 2018

  • Sharma, Prachi; Truhlar, Donald G.; Gagliardi, Laura
  • The Journal of Chemical Physics, Vol. 148, Issue 12
  • DOI: 10.1063/1.5021185

m -Benzyne and p -Benzyne
journal, March 1999

  • Sander, Wolfram
  • Accounts of Chemical Research, Vol. 32, Issue 8
  • DOI: 10.1021/ar960153k

Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications
journal, December 2011

  • Szalay, Péter G.; Müller, Thomas; Gidofalvi, Gergely
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200137a

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory
journal, January 2010

  • Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric
  • The Journal of Chemical Physics, Vol. 132, Issue 2
  • DOI: 10.1063/1.3275806

Use of benzynes for the synthesis of heterocycles
journal, January 2013

  • Dubrovskiy, Anton V.; Markina, Nataliya A.; Larock, Richard C.
  • Org. Biomol. Chem., Vol. 11, Issue 2
  • DOI: 10.1039/c2ob26673c

Full Correlation in a Multiconfigurational Study of Bimetallic Clusters: Restricted Active Space Pair-Density Functional Theory Study of [2Fe–2S] Systems
journal, April 2019

  • Presti, Davide; Stoneburner, Samuel J.; Truhlar, Donald G.
  • The Journal of Physical Chemistry C, Vol. 123, Issue 18
  • DOI: 10.1021/acs.jpcc.9b00222

Intramolecular Charge Transfer and Local Excitation in Organic Fluorescent Photoredox Catalysts Explained by RASCI-PDFT
journal, May 2018

  • Presti, Davide; Truhlar, Donald G.; Gagliardi, Laura
  • The Journal of Physical Chemistry C, Vol. 122, Issue 22
  • DOI: 10.1021/acs.jpcc.8b01844

Multiconfiguration second-order perturbation theory approach to strong electron correlation in chemistry and photochemistry: Multiconfiguration second-order perturbation theory
journal, November 2011

  • Roca-Sanjuán, Daniel; Aquilante, Francesco; Lindh, Roland
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 4
  • DOI: 10.1002/wcms.97

Multiconfiguration Pair-Density Functional Theory
journal, August 2014

  • Li Manni, Giovanni; Carlson, Rebecca K.; Luo, Sijie
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 9
  • DOI: 10.1021/ct500483t

Dynamical Self-energy Mapping (DSEM) for Creation of Sparse Hamiltonians Suitable for Quantum Computing
journal, November 2021

  • Dhawan, Diksha; Metcalf, Mekena; Zgid, Dominika
  • Journal of Chemical Theory and Computation, Vol. 17, Issue 12
  • DOI: 10.1021/acs.jctc.1c00931

Quantum Information and Algorithms for Correlated Quantum Matter
journal, December 2020

Role of Triplet States in the Photodynamics of Aniline
journal, April 2021

  • Lykhin, Aleksandr O.; Truhlar, Donald G.; Gagliardi, Laura
  • Journal of the American Chemical Society, Vol. 143, Issue 15
  • DOI: 10.1021/jacs.1c00989

Valence ππ* Excitations in Benzene Studied by Multiconfiguration Pair-Density Functional Theory
journal, December 2018

  • Sharma, Prachi; Bernales, Varinia; Truhlar, Donald G.
  • The Journal of Physical Chemistry Letters, Vol. 10, Issue 1
  • DOI: 10.1021/acs.jpclett.8b03277

Efficient algorithm for multiconfiguration pair-density functional theory with application to the heterolytic dissociation energy of ferrocene
journal, January 2017

  • Sand, Andrew M.; Truhlar, Donald G.; Gagliardi, Laura
  • The Journal of Chemical Physics, Vol. 146, Issue 3
  • DOI: 10.1063/1.4973709

Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware
journal, April 2020

  • Keen, Trevor; Maier, Thomas; Johnston, Steven
  • Quantum Science and Technology, Vol. 5, Issue 3
  • DOI: 10.1088/2058-9565/ab7d4c

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and the Double Unitary Coupled-Cluster Approach
journal, September 2020

  • Metcalf, Mekena; Bauman, Nicholas P.; Kowalski, Karol
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 10
  • DOI: 10.1021/acs.jctc.0c00421

Approximate solution for electron correlation through the use of Schwinger probes
journal, June 1998

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science
journal, October 2020

Resolving correlated states of benzyne with an error-mitigated contracted quantum eigensolver
journal, February 2022

Extended separated-pair approximation for transition metal potential energy curves
journal, March 2020

  • Li, Shuhang J.; Gagliardi, Laura; Truhlar, Donald G.
  • The Journal of Chemical Physics, Vol. 152, Issue 12
  • DOI: 10.1063/5.0003048

Electronic excited-state energies from a linear response theory based on the ground-state two-electron reduced density matrix
journal, March 2008

  • Greenman, Loren; Mazziotti, David A.
  • The Journal of Chemical Physics, Vol. 128, Issue 11
  • DOI: 10.1063/1.2890961

Application of fermionic marginal constraints to hybrid quantum algorithms
journal, May 2018

  • Rubin, Nicholas C.; Babbush, Ryan; McClean, Jarrod
  • New Journal of Physics, Vol. 20, Issue 5
  • DOI: 10.1088/1367-2630/aab919

Canonical transformation theory for multireference problems
journal, May 2006

  • Yanai, Takeshi; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 124, Issue 19
  • DOI: 10.1063/1.2196410

Cumulant reconstruction of the three-electron reduced density matrix in the anti-Hermitian contracted Schrödinger equation
journal, September 2007

  • DePrince, A. Eugene; Mazziotti, David A.
  • The Journal of Chemical Physics, Vol. 127, Issue 10
  • DOI: 10.1063/1.2768354

Calculation of Chemical Reaction Barrier Heights by Multiconfiguration Pair-Density Functional Theory with Correlated Participating Orbitals
journal, October 2019

  • Sand, Andrew M.; Kidder, Katherine M.; Truhlar, Donald G.
  • The Journal of Physical Chemistry A, Vol. 123, Issue 45
  • DOI: 10.1021/acs.jpca.9b08134

A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications
journal, April 1999

  • Mahapatra, Uttam Sinha; Datta, Barnali; Mukherjee, Debashis
  • The Journal of Chemical Physics, Vol. 110, Issue 13
  • DOI: 10.1063/1.478523

Reducing Qubit Requirements for Quantum Simulations Using Molecular Point Group Symmetries
journal, August 2020

  • Setia, Kanav; Chen, Richard; Rice, Julia E.
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 10
  • DOI: 10.1021/acs.jctc.0c00113

Quantum computing enhanced computational catalysis
journal, July 2021

Elucidating reaction mechanisms on quantum computers
journal, July 2017

  • Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 29
  • DOI: 10.1073/pnas.1619152114

Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion
journal, August 2020

  • Urbanek, Miroslav; Camps, Daan; Van Beeumen, Roel
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 9
  • DOI: 10.1021/acs.jctc.0c00447

Conical Intersection of the Ground and First Excited States of Water: Energies and Reduced Density Matrices from the Anti-Hermitian Contracted Schrödinger Equation
journal, December 2011

  • Snyder, James W.; Mazziotti, David A.
  • The Journal of Physical Chemistry A, Vol. 115, Issue 48
  • DOI: 10.1021/jp208013m

Multiconfiguration Pair-Density Functional Theory for Iron Porphyrin with CAS, RAS, and DMRG Active Spaces
journal, February 2019

  • Zhou, Chen; Gagliardi, Laura; Truhlar, Donald G.
  • The Journal of Physical Chemistry A, Vol. 123, Issue 15
  • DOI: 10.1021/acs.jpca.8b12479

State-interaction pair-density functional theory
journal, July 2018

  • Sand, Andrew M.; Hoyer, Chad E.; Truhlar, Donald G.
  • The Journal of Chemical Physics, Vol. 149, Issue 2
  • DOI: 10.1063/1.5036727

Magnetic Coupling in a Tris-hydroxo-Bridged Chromium Dimer Occurs through Ligand Mediated Superexchange in Conjunction with Through-Space Coupling
journal, September 2020

  • Sharma, Prachi; Truhlar, Donald G.; Gagliardi, Laura
  • Journal of the American Chemical Society, Vol. 142, Issue 39
  • DOI: 10.1021/jacs.0c06399

Decomposition of the Electronic Energy in Terms of Density, Density Coherence, and the Connected Part of the Two-Body Reduced Density Matrix
journal, August 2021

  • Zhang, Dayou; Truhlar, Donald G.
  • Journal of Chemical Theory and Computation, Vol. 17, Issue 9
  • DOI: 10.1021/acs.jctc.1c00679

Quantum Monte Carlo and Related Approaches
journal, December 2011

  • Austin, Brian M.; Zubarev, Dmitry Yu.; Lester, William A.
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr2001564

A New Mixing of Nonlocal Exchange and Nonlocal Correlation with Multiconfiguration Pair-Density Functional Theory
journal, November 2020

  • Pandharkar, Riddhish; Hermes, Matthew R.; Truhlar, Donald G.
  • The Journal of Physical Chemistry Letters, Vol. 11, Issue 23
  • DOI: 10.1021/acs.jpclett.0c02956

Accurate singlet–triplet gaps in biradicals via the spin averaged anti-Hermitian contracted Schrödinger equation
journal, April 2021

  • Boyn, Jan-Niklas; Mazziotti, David A.
  • The Journal of Chemical Physics, Vol. 154, Issue 13
  • DOI: 10.1063/5.0045007

New perspectives in multireference perturbation theory: the n-electron valence state approach
journal, December 2006

  • Angeli, Celestino; Pastore, Mariachiara; Cimiraglia, Renzo
  • Theoretical Chemistry Accounts, Vol. 117, Issue 5-6
  • DOI: 10.1007/s00214-006-0207-0

Ultraviolet Photoelectron Spectroscopy of the o -, m -, and p- Benzyne Negative Ions. Electron Affinities and Singlet−Triplet Splittings for o -, m -, and p -Benzyne
journal, June 1998

  • Wenthold, Paul G.; Squires, Robert R.; Lineberger, W. C.
  • Journal of the American Chemical Society, Vol. 120, Issue 21
  • DOI: 10.1021/ja9803355

Extraction of electronic excited states from the ground-state two-particle reduced density matrix
journal, November 2003

Multiconfiguration Pair-Density Functional Theory: A Fully Translated Gradient Approximation and Its Performance for Transition Metal Dimers and the Spectroscopy of Re 2 Cl 8 2–
journal, August 2015

  • Carlson, Rebecca K.; Truhlar, Donald G.; Gagliardi, Laura
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 9
  • DOI: 10.1021/acs.jctc.5b00609

Qiskit/qiskit-metapackage: Qiskit 0.44.0
software, July 2023

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    Ab initio Quantum Simulation of Strongly Correlated Materials with Quantum Embedding
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