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Title: Benchmarking Adaptive Variational Quantum Eigensolvers

Abstract

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H 2 , NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

Authors:
; ; ;
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division
OSTI Identifier:
1731007
Alternate Identifier(s):
OSTI ID: 1771891
Grant/Contract Number:  
3ERKCG12; AC05-00OR22725
Resource Type:
Published Article
Journal Name:
Frontiers in Chemistry
Additional Journal Information:
Journal Name: Frontiers in Chemistry Journal Volume: 8; Journal ID: ISSN 2296-2646
Publisher:
Frontiers Media SA
Country of Publication:
Switzerland
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; ADAPT-VQE; quantum computing; quantum chemistry; VQE; potential energy scan; state fidelity

Citation Formats

Claudino, Daniel, Wright, Jerimiah, McCaskey, Alexander J., and Humble, Travis S.. Benchmarking Adaptive Variational Quantum Eigensolvers. Switzerland: N. p., 2020. Web. https://doi.org/10.3389/fchem.2020.606863.
Claudino, Daniel, Wright, Jerimiah, McCaskey, Alexander J., & Humble, Travis S.. Benchmarking Adaptive Variational Quantum Eigensolvers. Switzerland. https://doi.org/10.3389/fchem.2020.606863
Claudino, Daniel, Wright, Jerimiah, McCaskey, Alexander J., and Humble, Travis S.. Fri . "Benchmarking Adaptive Variational Quantum Eigensolvers". Switzerland. https://doi.org/10.3389/fchem.2020.606863.
@article{osti_1731007,
title = {Benchmarking Adaptive Variational Quantum Eigensolvers},
author = {Claudino, Daniel and Wright, Jerimiah and McCaskey, Alexander J. and Humble, Travis S.},
abstractNote = {By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H 2 , NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.},
doi = {10.3389/fchem.2020.606863},
journal = {Frontiers in Chemistry},
number = ,
volume = 8,
place = {Switzerland},
year = {2020},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.3389/fchem.2020.606863

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Works referenced in this record:

Quantum computational chemistry
journal, March 2020


Exact parameterization of fermionic wave functions via unitary coupled cluster theory
journal, December 2019

  • Evangelista, Francesco A.; Chan, Garnet Kin-Lic; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 151, Issue 24
  • DOI: 10.1063/1.5133059

Multireference Nature of Chemistry: The Coupled-Cluster View
journal, December 2011

  • Lyakh, Dmitry I.; Musiał, Monika; Lotrich, Victor F.
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr2001417

Quantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver
journal, June 2019


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

On the limited memory BFGS method for large scale optimization
journal, August 1989

  • Liu, Dong C.; Nocedal, Jorge
  • Mathematical Programming, Vol. 45, Issue 1-3
  • DOI: 10.1007/BF01589116

New perspectives on unitary coupled-cluster theory
journal, January 2006

  • Taube, Andrew G.; Bartlett, Rodney J.
  • International Journal of Quantum Chemistry, Vol. 106, Issue 15
  • DOI: 10.1002/qua.21198

Towards a full CCSDT model for electron correlation
journal, October 1985

  • Urban, Miroslav; Noga, Jozef; Cole, Samuel J.
  • The Journal of Chemical Physics, Vol. 83, Issue 8
  • DOI: 10.1063/1.449067

Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals
journal, September 1969

  • Hehre, W. J.; Stewart, R. F.; Pople, J. A.
  • The Journal of Chemical Physics, Vol. 51, Issue 6
  • DOI: 10.1063/1.1672392

Quantum circuit learning
journal, September 2018


Validating quantum-classical programming models with tensor network simulations
journal, December 2018


Quantum Natural Gradient
journal, May 2020


Many – Body Methods in Chemistry and Physics
book, January 2009


Is the Trotterized UCCSD Ansatz Chemically Well-Defined?
journal, November 2019

  • Grimsley, Harper R.; Claudino, Daniel; Economou, Sophia E.
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 1
  • DOI: 10.1021/acs.jctc.9b01083

Quantum Computing Circuits and Devices
journal, June 2019

  • Humble, Travis S.; Thapliyal, Himanshu; Munoz-Coreas, Edgard
  • IEEE Design & Test, Vol. 36, Issue 3
  • DOI: 10.1109/MDAT.2019.2907130

Updating quasi-Newton matrices with limited storage
journal, September 1980


Self‐Consistent Molecular Orbital Methods. IV. Use of Gaussian Expansions of Slater‐Type Orbitals. Extension to Second‐Row Molecules
journal, March 1970

  • Hehre, W. J.; Ditchfield, R.; Stewart, R. F.
  • The Journal of Chemical Physics, Vol. 52, Issue 5
  • DOI: 10.1063/1.1673374

The theory of variational hybrid quantum-classical algorithms
journal, February 2016


Iterative Qubit Coupled Cluster Approach with Efficient Screening of Generators
journal, January 2020

  • Ryabinkin, Ilya G.; Lang, Robert A.; Genin, Scott N.
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 2
  • DOI: 10.1021/acs.jctc.9b01084

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

Coupled-cluster method for multideterminantal reference states
journal, October 1981


Quantum++: A modern C++ quantum computing library
journal, December 2018


A fifth-order perturbation comparison of electron correlation theories
journal, May 1989


Quantum Computing in the NISQ era and beyond
journal, August 2018


Molecular orbital theory of the properties of inorganic and organometallic compounds. 1. STO-NG basis sets for third-row main-group elements
journal, August 1980

  • Pietro, William J.; Levi, Beverly A.; Hehre, Warren J.
  • Inorganic Chemistry, Vol. 19, Issue 8
  • DOI: 10.1021/ic50210a005

Alternative coupled-cluster ansätze II. The unitary coupled-cluster method
journal, February 1989


A language and hardware independent approach to quantum–classical computing
journal, January 2018


Hartree-Fock on a superconducting qubit quantum computer
journal, August 2020


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

High-Performance Computing with Quantum Processing Units
journal, May 2017

  • Britt, Keith A.; Humble, Travis S.
  • ACM Journal on Emerging Technologies in Computing Systems, Vol. 13, Issue 3
  • DOI: 10.1145/3007651

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
journal, September 2017

  • Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan
  • Nature, Vol. 549, Issue 7671
  • DOI: 10.1038/nature23879

Error analysis and improvements of coupled-cluster theory
journal, January 1991


XACC: a system-level software infrastructure for heterogeneous quantum–classical computing
journal, February 2020

  • McCaskey, Alexander J.; Lyakh, Dmitry I.; Dumitrescu, Eugene F.
  • Quantum Science and Technology, Vol. 5, Issue 2
  • DOI: 10.1088/2058-9565/ab6bf6

�ber das Paulische �quivalenzverbot
journal, September 1928

  • Jordan, P.; Wigner, E.
  • Zeitschrift f�r Physik, Vol. 47, Issue 9-10
  • DOI: 10.1007/BF01331938

Quantum Chemistry in the Age of Quantum Computing
journal, August 2019


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