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Cited by 1,033Quantum Computing Algorithms and ArchitectureQuantum many-body systemsAdvanced Chemical Physics Studies

An adaptive variational algorithm for exact molecular simulations on a quantum computer

Open access
Grimsley, Harper R., Economou, Sophia E., Barnes, Edwin, Mayhall, Nicholas J.·2019·Nature Communications
DOI 10.1038/s41467-019-10988-2PMC PMC6614426
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Abstract

Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that, instead of fixing an ansatz upfront, grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.

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  • Compared to UCC, ADAPT-VQE produces significantly more compact states, resulting in shallower quantum circuits.

    “For instance, compared to the prototypical unitary coupled cluster (UCC) approach, [5] ADAPT-VQE produces significantly more compact states, [9] resulting in shallower quantum circuits.”

    From Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE (2026) · cites this paper as [9]

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  1. [1]Aspuru-Guzik A Dutoi AD Love PJ Head-Gordon M Simulated quantum computation of molecular energies Science 2005 309 1704 1707 10.1126/science.1113479 16151006 · DOI · Paper page
  2. [3]Cao, Y. et al. Quantum chemistry in the age of quantum computing. http://arxiv.org/abs/1812.09976 (2018). 31469277 · arXiv
  3. [4]Kitaev, A. Y. Quantum measurements and the Abelian stabilizer problem. arXiv e-prints. https://arxiv.org/abs/quant-ph/9511026 (1995). · arXiv
  4. [6]Lanyon BP Towards quantum chemistry on a quantum computer Nat. Chem. 2010 2 106 111 10.1038/nchem.483 21124400 · DOI · Paper page
  5. [8]Paesani S Experimental Bayesian quantum phase estimation on a silicon photonic chip Phys. Rev. Lett. 2017 118 100503 10.1103/PhysRevLett.118.100503 28339220 · DOI
  6. [17]Lee J Huggins WJ Head-Gordon M Whaley KB Generalized unitary coupled cluster wavefunctions for quantum computation J. Chem. Theory Comput. 2019 15 311 324 10.1021/acs.jctc.8b01004 30485748 · DOI · Paper page
  7. [19]Shen Y Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure Phys. Rev. A 2017 95 020501 10.1103/PhysRevA.95.020501 · DOI
  8. [21]Xia, R., Bian, T. & Kais, S. Electronic structure calculations and the Ising Hamiltonian. J. Phys. Chem. B122, 3384–3395 (2017). 29099600
  9. [22]Xia R Kais S Quantum machine learning for electronic structure calculations Nat. Commun. 2018 9 4195 10.1038/s41467-018-06598-z 30305624 PMC6180079 · DOI
  10. [23]Bartlett RJ Kucharski SA Noga J Alternative coupled-cluster ansätze II. The unitary coupled-cluster method Chem. Phys. Lett. 1989 155 133 140 10.1016/S0009-2614(89)87372-5 · DOI · Paper page
  11. [24]Kutzelnigg W Error analysis and improvements of coupled-cluster theory Theor. Chim. Acta 1991 80 349 386 10.1007/BF01117418 · DOI · Paper page
  12. [25]Taube AG Bartlett RJ New perspectives on unitary coupled-cluster theory Int. J. Quantum Chem. 2006 106 3393 3401 10.1002/qua.21198 · DOI · Paper page
  13. [26]Harsha G Shiozaki T Scuseria GE On the difference between variational and unitary coupled cluster theories J. Chem. Phys. 2018 148 044107 10.1063/1.5011033 29390817 · DOI
  14. [28]Nakatsuji H Ehara M Iterative CI general singles and doubles (ICIGSD) method for calculating the exact wave functions of the ground and excited states of molecules J. Chem. Phys. 2005 122 194108 10.1063/1.1898207 16161564 · DOI
  15. [29]Nakatsuji H Structure of the exact wave function J. Chem. Phys. 2000 113 2949 10.1063/1.1287275 · DOI
  16. [30]Nakatsuji H Ehara M Structure of the exact wave function. V. Iterative configuration interaction method for molecular systems within finite basis J. Chem. Phys. 2002 117 9 12 10.1063/1.1487830 · DOI
  17. [31]Nakatsuji H Davidson ER Structure of the exact wave function. II. Iterative configuration interaction method J. Chem. Phys. 2001 115 2000 2006 10.1063/1.1383032 · DOI
  18. [32]Nooijen M Can the eigenstates of a many-body Hamiltonian be represented exactly using a general two-body cluster expansion? Phys. Rev. Lett. 2000 84 2108 2111 10.1103/PhysRevLett.84.2108 11017220 · DOI
  19. [33]Ryabinkin IG Yen T-C Genin SN Izmaylov AF Qubit coupled-cluster method: a systematic approach to quantum chemistry on a quantum computer J. Chem. Theory Comput. 2018 14 6317 6326 10.1021/acs.jctc.8b00932 30427679 · DOI · Paper page
  20. [34]Hatano, N. & Suzuki, M. Finding Exponential Product Formulas of Higher Orders. 37–68 (Springer, Berlin, Heidelberg, 2005).
  21. [35]Barkoutsos PK Quantum algorithms for electronic structure calculations: particle-hole Hamiltonian and optimized wave-function expansions Phys. Rev. A 2018 98 022322 10.1103/PhysRevA.98.022322 · DOI · Paper page
  22. [36]Turney JM Psi4: an open-source ab initio electronic structure program Wiley Interdiscip. Rev. Comput. Mol. Sci. 2012 2 556 565 10.1002/wcms.93 · DOI
  23. [37]Smith DGA Psi4NumPy: an interactive quantum chemistry programming environment for reference implementations and rapid development J. Chem. Theory Comput. 2018 14 3504 3511 10.1021/acs.jctc.8b00286 29771539 · DOI
  24. [38]McClean, J. R. et al. OpenFermion: the electronic structure package for quantum computers. http://arxiv.org/abs/1710.07629 (2017). · arXiv
  25. [40]Harrison RJ Approximating full configuration interaction with selected configuration interaction and perturbation theory J. Chem. Phys. 1991 94 5021 5031 10.1063/1.460537 · DOI
  26. [41]Povill A Rubio J Illas F Treating large intermediate spaces in the CIPSI method through a direct selected CI algorithm Theor. Chim. Acta 1992 82 229 238 10.1007/BF01113255 · DOI
  27. [42]Peris G Planelles J Malrieu J-P Paldus J Perturbatively selected CI as an optimal source for externally corrected CCSD J. Chem. Phys. 1999 110 11708 10.1063/1.479116 · DOI
  28. [43]Evangelista FA Adaptive multiconfigurational wave functions J. Chem. Phys. 2014 140 124114 10.1063/1.4869192 24697431 · DOI
  29. [44]Schriber JB Evangelista FA Communication: an adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy J. Chem. Phys. 2016 144 161106 10.1063/1.4948308 27131524 · DOI
  30. [45]Holmes AA Tubman NM Umrigar CJ Heat-bath configuration interaction: an efficient selected configuration interaction algorithm inspired by heat-bath sampling J. Chem. Theory Comput. 2016 12 3674 3680 10.1021/acs.jctc.6b00407 27428771 · DOI
  31. [46]Xu E Uejima M Ten-No SL Full coupled-cluster reduction for accurate description of strong electron correlation Phys. Rev. Lett. 2018 121 113001 10.1103/PhysRevLett.121.113001 30265114 · DOI
  32. [47]Lyakh DI Bartlett RJ An adaptive coupled-cluster theory: @CC approach J. Chem. Phys. 2010 133 244112 10.1063/1.3515476 21197981 · DOI
  33. [48]Bischoff FA Valeev EF Computing molecular correlation energies with guaranteed precision J. Chem. Phys. 2013 139 114106 10.1063/1.4820404 24070278 · DOI
  34. [49]Laikov DN Intrinsic minimal atomic basis representation of molecular electronic wavefunctions Int. J. Quantum Chem. 2011 111 2851 2867 10.1002/qua.22767 · DOI
  35. [50]Lu WC Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals J. Chem. Phys. 2004 120 2629 2637 10.1063/1.1638731 15268406 · DOI
  36. [51]Berghold G Parrinello M Hutter J Polarized atomic orbitals for linear scaling methods J. Chem. Phys. 2002 116 1800 1810 10.1063/1.1431270 · DOI
  37. [52]Lee MS Head-Gordon M Polarized atomic orbitals for self-consistent field electronic structure calculations J. Chem. Phys. 1998 107 9085 10.1063/1.475199 · DOI
  38. [53]Schütt O VandeVondele J Machine learning adaptive basis sets for efficient large scale density functional theory simulation J. Chem. Theory Comput. 2018 14 4168 4175 10.1021/acs.jctc.8b00378 29957943 PMC6096449 · DOI
  39. [54]Evangelista FA Hanauer M Köhn A Gauss J A sequential transformation approach to the internally contracted multireference coupled cluster method J. Chem. Phys. 2012 136 204108 10.1063/1.4718704 22667541 · DOI

Cited by

Sorted by citations

Authors
Grimsley, H. R., Economou, S. E., Barnes, E., & Mayhall, N. J.
Affiliations
Virginia Tech (US)
Corresponding author
Mayhall, Nicholas J.
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2019-07-08
Volume
10
Issue
1
Pages
3007-3007
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-019-10988-2
PMC
PMC6614426
OpenAlex
W2954369586
Cited by
1,033
References
13
Citations by year
2026: 133 · 2025: 200 · 2024: 204 · 2023: 155 · 2022: 133 · 2021: 138 · 2020: 58 · 2019: 12
FWCI
39.01
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by)
  • arXiv (Cornell University) (publishedVersion)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • VTechWorks (Virginia Tech) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • U.S. Department of Energy (DE-SC0019199, DE-SC0019318)
  • National Science Foundation (1839136)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
Keywords
variational quantum eigensolver, quantum chemistry simulation, quantum computing, strongly correlated molecules, circuit depth, unitary coupled cluster, chemical accuracy, variational algorithms

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