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Nykänen A, Miller A, Talarico W, Knecht S, Kovyrshin A, Skogh M, Tornberg L, Broo A, Mensa S, Symons BCB, Sahin E, Crain J, Tavernelli I, Pavošević F. Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals. J Chem Theory Comput 2023; 19:9269-9277. [PMID: 38081802 DOI: 10.1021/acs.jctc.3c01091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2023]
Abstract
Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.
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Affiliation(s)
- Anton Nykänen
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
| | - Aaron Miller
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
- School of Physics, Trinity College Dublin, College Green Dublin 2, Ireland
| | - Walter Talarico
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
- Department of Applied Physics, QTF Centre of Excellence, Center for Quantum Engineering, Aalto University School of Science, Aalto FIN-00076, Finland
| | - Stefan Knecht
- Algorithmiq Ltd., Kanavakatu 3C, Helsinki FI-00160, Finland
- ETH Zürich, Department of Chemistry and Applied Life Sciences Vladimir-Prelog-Weg 1-5/10, Zürich 8093, Switzerland
| | - Arseny Kovyrshin
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Mårten Skogh
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Gothenburg 412 96, Sweden
| | - Lars Tornberg
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Anders Broo
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Stefano Mensa
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, U.K
| | | | - Emre Sahin
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, U.K
| | - Jason Crain
- IBM Research Europe, Hartree Centre STFC Laboratory, Sci-Tech Daresbury, Warrington WA4 4AD, U.K
- Department of Biochemistry, University of Oxford, Oxford OX1 3QU, U.K
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Kovyrshin A, Skogh M, Tornberg L, Broo A, Mensa S, Sahin E, Symons BCB, Crain J, Tavernelli I. Nonadiabatic Nuclear-Electron Dynamics: A Quantum Computing Approach. J Phys Chem Lett 2023; 14:7065-7072. [PMID: 37527463 DOI: 10.1021/acs.jpclett.3c01589] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/03/2023]
Abstract
Coupled quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling. Consequently, quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for simulating the time-evolution of molecular systems and apply it to proton transfer dynamics in malonaldehyde, described as a rigid scaffold. The proposed quantum algorithm can be easily generalized to include the explicit dynamics of the classically described molecular scaffold. We show how entanglement between electronic and nuclear degrees of freedom can persist over long times if electrons do not follow the nuclear displacement adiabatically. The proposed quantum algorithm may become a valid candidate for the study of such phenomena when sufficiently powerful quantum computers become available.
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Affiliation(s)
- Arseny Kovyrshin
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Mårten Skogh
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Lars Tornberg
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Anders Broo
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Stefano Mensa
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Emre Sahin
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Benjamin C B Symons
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Jason Crain
- IBM Research Europe, Hartree Centre STFC Laboratory, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
- Department of Biochemistry, University of Oxford, Oxford OX1 3QU, U.K
| | - Ivano Tavernelli
- IBM Quantum, IBM Research Europe-Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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Kovyrshin A, Skogh M, Broo A, Mensa S, Sahin E, Crain J, Tavernelli I. A quantum computing implementation of nuclearelectronic orbital (NEO) theory: Toward an exact pre-Born-Oppenheimer formulation of molecular quantum systems. J Chem Phys 2023; 158:2894412. [PMID: 37272571 DOI: 10.1063/5.0150291] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2023] [Accepted: 05/16/2023] [Indexed: 06/06/2023] Open
Abstract
Nuclear quantum phenomena beyond the Born-Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient implementation of coupled electron-nuclear quantum dynamics, it is recognized that these problems scale exponentially with system size on classical processors and, therefore, may benefit from quantum computing implementations. Here, we introduce a methodology for the efficient quantum treatment of the electron-nuclear problem on near-term quantum computers, based upon the Nuclear-Electronic Orbital (NEO) approach. We generalize the electronic two-qubit tapering scheme to include nuclei by exploiting symmetries inherent in the NEO framework, thereby reducing the Hamiltonian dimension, number of qubits, gates, and measurements needed for calculations. We also develop parameter transfer and initialization techniques, which improve convergence behavior relative to conventional initialization. These techniques are applied to H2 and malonaldehyde for which results agree with NEO full configuration interaction and NEO complete active space configuration interaction benchmarks for ground state energy to within 10-6 hartree and entanglement entropy to within 10-4. These implementations therefore significantly reduce resource requirements for full quantum simulations of molecules on near-term quantum devices while maintaining high accuracy.
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Affiliation(s)
- Arseny Kovyrshin
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Mårten Skogh
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Gothenburg, Sweden
| | - Anders Broo
- Data Science and Modelling, Pharmaceutical Sciences, R&D, AstraZeneca Gothenburg, Pepparedsleden 1, Molndal SE-431 83, Sweden
| | - Stefano Mensa
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Emre Sahin
- The Hartree Centre, STFC, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Jason Crain
- IBM Research Europe, Hartree Centre STFC Laboratory, Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
- Department of Biochemistry, University of Oxford, Oxford OX1 3QU, United Kingdom
| | - Ivano Tavernelli
- IBM Quantum, IBM Research Europe - Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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Affiliation(s)
- Arseny Kovyrshin
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Knecht S, Hedegård ED, Keller S, Kovyrshin A, Ma Y, Muolo A, Stein CJ, Reiher M. New Approaches for ab initio Calculations of Molecules with Strong Electron Correlation. Chimia (Aarau) 2016; 70:244-51. [DOI: 10.2533/chimia.2016.244] [Citation(s) in RCA: 79] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
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Abstract
Analytical excitation-energy gradients from frozen-density embedding–time-dependent density functional theory are derived and implemented, which are important for photochemistry in complex systems.
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Affiliation(s)
- Arseny Kovyrshin
- Laboratorium für Physikalische Chemie
- ETH Zürich
- 8093 Zürich
- Switzerland
| | - Johannes Neugebauer
- Theoretische Organische Chemie
- Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation
- Westfälische Wilhelms-Universität Münster
- 48149 Münster
- Germany
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Kovyrshin A, Angelis FD, Neugebauer J. Selective TDDFT with automatic removal of ghost transitions: application to a perylene-dye-sensitized solar cell model. Phys Chem Chem Phys 2012; 14:8608-19. [DOI: 10.1039/c2cp40840f] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Kovyrshin A, Neugebauer J. State-selective optimization of local excited electronic states in extended systems. J Chem Phys 2010; 133:174114. [DOI: 10.1063/1.3488230] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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