Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Abstract

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and onlymore » a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.« less

Authors:
ORCiD logo [1]; ORCiD logo [2];  [2]; ORCiD logo [2]; ORCiD logo [1];  [1]; ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
  2. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
2318949
Report Number(s):
LA-UR-22-20462
Journal ID: ISSN 1549-9618
Grant/Contract Number:  
89233218CNA000001; 20200056DR
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 18; Journal Issue: 9; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Kumar, Ashutosh, Asthana, Ayush, Masteran, Conner, Valeev, Edward F., Zhang, Yu, Cincio, Lukasz, Tretiak, Sergei, and Dub, Pavel A. Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits. United States: N. p., 2022. Web. doi:10.1021/acs.jctc.2c00520.
Copy to clipboard
Kumar, Ashutosh, Asthana, Ayush, Masteran, Conner, Valeev, Edward F., Zhang, Yu, Cincio, Lukasz, Tretiak, Sergei, & Dub, Pavel A. Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits. United States. https://doi.org/10.1021/acs.jctc.2c00520
Copy to clipboard
Kumar, Ashutosh, Asthana, Ayush, Masteran, Conner, Valeev, Edward F., Zhang, Yu, Cincio, Lukasz, Tretiak, Sergei, and Dub, Pavel A. Fri . "Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits". United States. https://doi.org/10.1021/acs.jctc.2c00520. https://www.osti.gov/servlets/purl/2318949.
Copy to clipboard
@article{osti_2318949,
title = {Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits},
author = {Kumar, Ashutosh and Asthana, Ayush and Masteran, Conner and Valeev, Edward F. and Zhang, Yu and Cincio, Lukasz and Tretiak, Sergei and Dub, Pavel A.},
abstractNote = {Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.},
doi = {10.1021/acs.jctc.2c00520},
journal = {Journal of Chemical Theory and Computation},
number = 9,
volume = 18,
place = {United States},
year = {Fri Aug 19 00:00:00 EDT 2022},
month = {Fri Aug 19 00:00:00 EDT 2022}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1021/acs.jctc.2c00520
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

The Determination of Energies and Wavefunctions with Full Electronic Correlation
journal, April 1969

  • Boys, S. F.; Handy, N. C.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 310, Issue 1500
  • DOI: 10.1098/rspa.1969.0061

Spinfree formulation of reduced density matrices, density cumulants and generalised normal ordering
journal, February 2010

  • Kutzelnigg, Werner; Shamasundar, K. R.; Mukherjee, Debashis
  • Molecular Physics, Vol. 108, Issue 3-4
  • DOI: 10.1080/00268970903547926

Quantum simulations of excited states with active-space downfolded Hamiltonians
journal, December 2019

  • Bauman, Nicholas P.; Low, Guang Hao; Kowalski, Karol
  • The Journal of Chemical Physics, Vol. 151, Issue 23
  • DOI: 10.1063/1.5128103

Multiresolution quantum chemistry: Basic theory and initial applications
journal, December 2004

  • Harrison, Robert J.; Fann, George I.; Yanai, Takeshi
  • The Journal of Chemical Physics, Vol. 121, Issue 23
  • DOI: 10.1063/1.1791051

Stationary perturbation theory: I. Survey of basic concepts
journal, January 1992

New correlation factors for explicitly correlated electronic wave functions
journal, August 2005

  • Tew, David P.; Klopper, Wim
  • The Journal of Chemical Physics, Vol. 123, Issue 7
  • DOI: 10.1063/1.1999632

Optimized complementary auxiliary basis sets for explicitly correlated methods: aug-cc-pVnZ orbital basis sets
journal, July 2009

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons
journal, February 2020

  • Stair, Nicholas H.; Huang, Renke; Evangelista, Francesco A.
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 4
  • DOI: 10.1021/acs.jctc.9b01125

Alternative formulation of the matrix elements in MP2-R12 theory
journal, January 2005

  • Kedžuch, Stanislav; Milko, Matúš; Noga, Jozef
  • International Journal of Quantum Chemistry, Vol. 105, Issue 6
  • DOI: 10.1002/qua.20744

Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm
journal, February 2018

A variational eigenvalue solver on a photonic quantum processor
journal, July 2014

  • Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms5213

SF-[2]R12: A spin-adapted explicitly correlated method applicable to arbitrary electronic states
journal, December 2011

  • Kong, Liguo; Valeev, Edward F.
  • The Journal of Chemical Physics, Vol. 135, Issue 21
  • DOI: 10.1063/1.3664729

Downfolding of many-body Hamiltonians using active-space models: Extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
journal, July 2019

  • Bauman, Nicholas P.; Bylaska, Eric J.; Krishnamoorthy, Sriram
  • The Journal of Chemical Physics, Vol. 151, Issue 1
  • DOI: 10.1063/1.5094643

Qiskit: An Open-source Framework for Quantum Computing
software, January 2019

Quasi-degenerate perturbation theory withgeneral multiconfiguration self-consistent field reference functions
journal, June 2002

  • Nakano, Haruyuki; Uchiyama, Ryuma; Hirao, Kimihiko
  • Journal of Computational Chemistry, Vol. 23, Issue 12
  • DOI: 10.1002/jcc.10050

Explicitly Correlated Electrons in Molecules
journal, December 2011

  • Hättig, Christof; Klopper, Wim; Köhn, Andreas
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200168z

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

Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
journal, December 1999

Extensions of r12 corrections to CC2-R12 for excited states
journal, August 2006

  • Neiss, Christian; Hättig, Christof; Klopper, Wim
  • The Journal of Chemical Physics, Vol. 125, Issue 6
  • DOI: 10.1063/1.2335443

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms
journal, May 2021

  • Yeter‐Aydeniz, Kübra; Gard, Bryan T.; Jakowski, Jacek
  • Advanced Quantum Technologies, Vol. 4, Issue 7
  • DOI: 10.1002/qute.202100012

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory
journal, January 2016

  • Riplinger, Christoph; Pinski, Peter; Becker, Ute
  • The Journal of Chemical Physics, Vol. 144, Issue 2
  • DOI: 10.1063/1.4939030

Generalized Unitary Coupled Cluster Wave functions for Quantum Computation
journal, November 2018

  • Lee, Joonho; Huggins, William J.; Head-Gordon, Martin
  • Journal of Chemical Theory and Computation, Vol. 15, Issue 1
  • DOI: 10.1021/acs.jctc.8b01004

Adiabatic Quantum Simulation of Quantum Chemistry
journal, October 2014

  • Babbush, Ryan; Love, Peter J.; Aspuru-Guzik, Alán
  • Scientific Reports, Vol. 4, Issue 1
  • DOI: 10.1038/srep06603

Unitary Selective Coupled-Cluster Method
text, January 2021

Qubit-ADAPT-VQE: An Adaptive Algorithm for Constructing Hardware-Efficient Ansätze on a Quantum Processor
journal, April 2021

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz
journal, October 2018

  • Romero, Jonathan; Babbush, Ryan; McClean, Jarrod R.
  • Quantum Science and Technology, Vol. 4, Issue 1
  • DOI: 10.1088/2058-9565/aad3e4

Coupled‐cluster calculations of the excitation energies of ethylene, butadiene, and cyclopentadiene
journal, October 1996

  • Watts, John D.; Gwaltney, Steven R.; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 105, Issue 16
  • DOI: 10.1063/1.471988

Quantum Krylov subspace algorithms for ground and excited state energy estimation
text, January 2021

New Relativistic ANO Basis Sets for Transition Metal Atoms
journal, July 2005

  • Roos, Björn O.; Lindh, Roland; Malmqvist, Per-Åke
  • The Journal of Physical Chemistry A, Vol. 109, Issue 29
  • DOI: 10.1021/jp0581126

Simulated Quantum Computation of Molecular Energies
journal, September 2005

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
journal, April 2001

Canonical transformation theory from extended normal ordering
journal, September 2007

  • Yanai, Takeshi; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 127, Issue 10
  • DOI: 10.1063/1.2761870

Variational Quantum Eigensolver with Reduced Circuit Complexity
text, January 2021

Explicitly correlated coupled cluster method for accurate treatment of open-shell molecules with hundreds of atoms
journal, September 2020

  • Kumar, Ashutosh; Neese, Frank; Valeev, Edward F.
  • The Journal of Chemical Physics, Vol. 153, Issue 9
  • DOI: 10.1063/5.0012753

Quantum Davidson Algorithm for Excited States
preprint, January 2022

Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in the Variational Quantum Eigensolver
journal, June 2021

Explicitly Correlated R12/F12 Methods for Electronic Structure
journal, December 2011

  • Kong, Liguo; Bischoff, Florian A.; Valeev, Edward F.
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200204r

On the eigenfunctions of many-particle systems in quantum mechanics
journal, January 1957

Quantum Monte Carlo study of the transcorrelated method for correlation factors
journal, February 2010

  • Luo, Hongjun; Hackbusch, Wolfgang; Flad, Heinz-Jürgen
  • Molecular Physics, Vol. 108, Issue 3-4
  • DOI: 10.1080/00268970903521194

Normal order and extended Wick theorem for a multiconfiguration reference wave function
journal, July 1997

  • Kutzelnigg, Werner; Mukherjee, Debashis
  • The Journal of Chemical Physics, Vol. 107, Issue 2
  • DOI: 10.1063/1.474405

Explicitly correlated second order perturbation theory: Introduction of a rational generator and numerical quadratures
journal, January 2004

  • Ten-no, Seiichiro
  • The Journal of Chemical Physics, Vol. 121, Issue 1
  • DOI: 10.1063/1.1757439

Correct Quantum Chemistry in a Minimal Basis from Effective Hamiltonians
journal, January 2016

  • Watson, Thomas J.; Chan, Garnet Kin-Lic
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 2
  • DOI: 10.1021/acs.jctc.5b00138

Simulating physics with computers
journal, June 1982

  • Feynman, Richard P.
  • International Journal of Theoretical Physics, Vol. 21, Issue 6-7
  • DOI: 10.1007/BF02650179

Quantum Filter Diagonalization with Compressed Double-Factorized Hamiltonians
journal, December 2021

Explicitly correlated electronic structure theory from R12/F12 ansätze: Explicitly correlated electronic structure theory
journal, May 2011

  • Ten-no, Seiichiro; Noga, Jozef
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 1
  • DOI: 10.1002/wcms.68

A feasible transcorrelated method for treating electronic cusps using a frozen Gaussian geminal
journal, November 2000

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

Regularized orbital-optimized second-order perturbation theory
journal, December 2013

  • Stück, David; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 139, Issue 24
  • DOI: 10.1063/1.4851816

Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
journal, November 2019

Universal perturbative explicitly correlated basis set incompleteness correction
journal, November 2009

  • Torheyden, Martin; Valeev, Edward F.
  • The Journal of Chemical Physics, Vol. 131, Issue 17
  • DOI: 10.1063/1.3254836

Nonclassical terms in the true effective valence shell Hamiltonian: A second quantized formalism
journal, August 1976

  • Iwata, Suehiro; Freed, Karl F.
  • The Journal of Chemical Physics, Vol. 65, Issue 3
  • DOI: 10.1063/1.433170

An Introduction to Coupled Cluster Theory for Computational Chemists
book, January 2000

  • Crawford, T. Daniel; Schaefer, Henry F.; Lipkowitz, Kenny B.
  • Reviews in Computational Chemistry: Lipkowitz/Reviews
  • DOI: 10.1002/9780470125915.ch2

Coupled-cluster response theory with linear-r12 corrections: The CC2-R12 model for excitation energies
journal, January 2006

  • Fliegl, Heike; Hättig, Christof; Klopper, Wim
  • The Journal of Chemical Physics, Vol. 124, Issue 4
  • DOI: 10.1063/1.2161183

Array programming with NumPy
journal, September 2020

  • Harris, Charles R.; Millman, K. Jarrod; van der Walt, Stéfan J.
  • Nature, Vol. 585, Issue 7825
  • DOI: 10.1038/s41586-020-2649-2

An efficient adaptive variational quantum solver of the Schrödinger equation based on reduced density matrices
journal, June 2021

  • Liu, Jie; Li, Zhenyu; Yang, Jinlong
  • The Journal of Chemical Physics, Vol. 154, Issue 24
  • DOI: 10.1063/5.0054822

Computing molecular excited states on a D-Wave quantum annealer
journal, September 2021

  • Teplukhin, Alexander; Kendrick, Brian K.; Mniszewski, Susan M.
  • Scientific Reports, Vol. 11, Issue 1
  • DOI: 10.1038/s41598-021-98331-y

Reducing Qubit Requirements while Maintaining Numerical Precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach
journal, January 2021

  • Kottmann, Jakob S.; Schleich, Philipp; Tamayo-Mendoza, Teresa
  • The Journal of Physical Chemistry Letters, Vol. 12, Issue 1
  • DOI: 10.1021/acs.jpclett.0c03410

r 12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l
journal, December 1985

Low rank representations for quantum simulation of electronic structure
journal, May 2021

Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
journal, October 2020

Quantum simulation of electronic structure with a transcorrelated Hamiltonian: improved accuracy with a smaller footprint on the quantum computer
journal, January 2020

  • Motta, Mario; Gujarati, Tanvi P.; Rice, Julia E.
  • Physical Chemistry Chemical Physics, Vol. 22, Issue 42
  • DOI: 10.1039/D0CP04106H

Explicitly correlated coupled-cluster theory using cusp conditions. I. Perturbation analysis of coupled-cluster singles and doubles (CCSD-F12)
journal, November 2010

  • Köhn, Andreas; Tew, David P.
  • The Journal of Chemical Physics, Vol. 133, Issue 17
  • DOI: 10.1063/1.3496372

Prediction of Reaction Barriers and Thermochemical Properties with Explicitly Correlated Coupled-Cluster Methods: A Basis Set Assessment
journal, August 2012

  • Zhang, Jinmei; Valeev, Edward F.
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 9
  • DOI: 10.1021/ct3005547

Canonical transcorrelated theory with projected Slater-type geminals
journal, February 2012

  • Yanai, Takeshi; Shiozaki, Toru
  • The Journal of Chemical Physics, Vol. 136, Issue 8
  • DOI: 10.1063/1.3688225

Optimized auxiliary basis sets for explicitly correlated methods
journal, November 2008

  • Yousaf, Kazim E.; Peterson, Kirk A.
  • The Journal of Chemical Physics, Vol. 129, Issue 18
  • DOI: 10.1063/1.3009271

Recent developments in the P y SCF program package
journal, July 2020

  • Sun, Qiming; Zhang, Xing; Banerjee, Samragni
  • The Journal of Chemical Physics, Vol. 153, Issue 2
  • DOI: 10.1063/5.0006074

An adaptive variational algorithm for exact molecular simulations on a quantum computer
journal, July 2019

    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: