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Burton HGA, Dong SS, Ghosh S, Gu B, Jackson NE, Keefer D, Lu Y, Monroe JI, Peng B, Pieri E, Spackman PR, Vacher M, Vuckovic S, Williams-Young D, Yang ZJ, Yue S, Zerze GH, Zhu T. JCTC Early Career Board Selects. J Chem Theory Comput 2024; 20:5785-5787. [PMID: 39039974 DOI: 10.1021/acs.jctc.4c00787] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/24/2024]
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Zhao S, Tang D, Xiao X, Wang R, Sun Q, Chen Z, Cai X, Li Z, Yu H, Fang WH. Quantum Computation of Conical Intersections on a Programmable Superconducting Quantum Processor. J Phys Chem Lett 2024; 15:7244-7253. [PMID: 38976358 DOI: 10.1021/acs.jpclett.4c01314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
Conical intersections (CIs) are pivotal in many photochemical processes. Traditional quantum chemistry methods, such as the state-average multiconfigurational methods, face computational hurdles in solving the electronic Schrödinger equation within the active space on classical computers. While quantum computing offers a potential solution, its feasibility in studying CIs, particularly on real quantum hardware, remains largely unexplored. Here, we present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent field method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a superconducting quantum processor. This approach is applied to investigate CIs in two prototypical systems─ethylene (C2H4) and triatomic hydrogen (H3). We illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic enhancements, can lead to a correct description of CIs on existing quantum devices. These results lay the groundwork for exploring the potential of quantum computing to study CIs in more complex systems in the future.
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Affiliation(s)
- Shoukuan Zhao
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Diandong Tang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Xiaoxiao Xiao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Ruixia Wang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Qiming Sun
- Quantum Engine LLC, Lacey, Washington 98516, United States
| | - Zhen Chen
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Xiaoxia Cai
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Haifeng Yu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Hefei National Laboratory, Hefei 230088, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education College of Chemistry, Beijing Normal University, Beijing 100875, China
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3
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Wang Y, Mazziotti DA. Quantum simulation of conical intersections. Phys Chem Chem Phys 2024; 26:11491-11497. [PMID: 38587679 DOI: 10.1039/d4cp00391h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/09/2024]
Abstract
We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H3+ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schrödinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.
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Affiliation(s)
- Yuchen Wang
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
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4
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Coe JP. Analytic Non-adiabatic Couplings for Selected Configuration Interaction via Approximate Degenerate Coupled Perturbed Hartree-Fock. J Chem Theory Comput 2023; 19:8053-8065. [PMID: 37939698 PMCID: PMC10687870 DOI: 10.1021/acs.jctc.3c00601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Revised: 10/24/2023] [Accepted: 10/25/2023] [Indexed: 11/10/2023]
Abstract
We use degenerate perturbation theory and assume that for degenerate pairs of orbitals, the coupled perturbed Hartree-Fock coefficients are symmetric in the degenerate basis to show [Formula: see text] is the only modification needed in the original molecular orbital basis. This enables us to develop efficient and accurate analytic nonadiabatic couplings between electronic states for selected configuration interactions (CIs). Even when the states belong to different irreducible representations, degenerate orbital pairs cannot be excluded by symmetry. For various excited states of carbon monoxide and trigonal planar ammonia, we benchmark the method against the full CI and find it to be accurate. We create a semi-numerical approach and use it to show that the analytic approach is correct even when a high-symmetry structure is distorted to break symmetry so that near degeneracies in orbitals occur. For a range of geometries of trigonal planar ammonia, we find that the analytic non-adiabatic couplings for selected CI can achieve sufficient accuracy using a small fraction of the full CI space.
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Affiliation(s)
- Jeremy P. Coe
- Institute of Chemical Sciences, School
of Engineering and Physical Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, U.K.
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5
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Lai J, Fan Y, Fu Q, Li Z, Yang J. Accurate and efficient calculations of Hellmann-Feynman forces for quantum computation. J Chem Phys 2023; 159:114113. [PMID: 37724727 DOI: 10.1063/5.0167444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 08/31/2023] [Indexed: 09/21/2023] Open
Abstract
First-order derivatives of energies with respect to atomic coordinates are widely computed and used in quantum chemistry simulations. The rapidly emerging technology of quantum computing offers a new paradigm for solving relevant quantum chemistry equations. In this work, we have achieved analytical calculations of atomic forces based on the Hellmann-Feynman theorem within the framework of the variational quantum eigensolver. The accuracy of the approach is demonstrated by calculating the atomic forces of H2, LiH, H2O, and NH3 molecules, which are in excellent agreement with values obtained from full configuration interaction calculations. In particular, for systems with degenerate molecular orbitals, the analytical approach has a significant accuracy advantage over finite-difference-based methods and will not involve additional computational effort on a quantum computer. The calculated forces are further used to optimize the geometries of NH3 and CH4 molecules and to perform ab initio molecular dynamics simulations for the umbrella inversion of NH3, demonstrating the feasibility of the approach in practical quantum chemistry simulations.
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Affiliation(s)
- Juntao Lai
- School of Future Technology, University of Science and Technology of China, Hefei 230026, China
| | - Yi Fan
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Qiang Fu
- School of Future Technology, University of Science and Technology of China, Hefei 230026, China
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Zhenyu Li
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jinlong Yang
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China
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6
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Hohenstein EG, Oumarou O, Al-Saadon R, Anselmetti GLR, Scheurer M, Gogolin C, Parrish RM. Efficient quantum analytic nuclear gradients with double factorization. J Chem Phys 2023; 158:114119. [PMID: 36948843 DOI: 10.1063/5.0137167] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/03/2023] Open
Abstract
Efficient representations of the Hamiltonian, such as double factorization, drastically reduce the circuit depth or the number of repetitions in error corrected and noisy intermediate-scale quantum (NISQ) algorithms for chemistry. We report a Lagrangian-based approach for evaluating relaxed one- and two-particle reduced density matrices from double factorized Hamiltonians, unlocking efficiency improvements in computing the nuclear gradient and related derivative properties. We demonstrate the accuracy and feasibility of our Lagrangian-based approach to recover all off-diagonal density matrix elements in classically simulated examples with up to 327 quantum and 18 470 total atoms in QM/MM simulations with modest-sized quantum active spaces. We show this in the context of the variational quantum eigensolver in case studies, such as transition state optimization, ab initio molecular dynamics simulation, and energy minimization of large molecular systems.
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Sugisaki K, Wakimoto H, Toyota K, Sato K, Shiomi D, Takui T. Quantum Algorithm for Numerical Energy Gradient Calculations at the Full Configuration Interaction Level of Theory. J Phys Chem Lett 2022; 13:11105-11111. [PMID: 36444985 PMCID: PMC9743205 DOI: 10.1021/acs.jpclett.2c02737] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 11/07/2022] [Indexed: 06/16/2023]
Abstract
A Bayesian phase difference estimation (BPDE) algorithm allows us to compute the energy gap of two electronic states of a given Hamiltonian directly by utilizing the quantum superposition of their wave functions. Here we report an extension of the BPDE algorithm to the direct calculation of the energy difference of two molecular geometries. We apply the BPDE algorithm for the calculation of numerical energy gradients based on the two-point finite-difference method, enabling us to execute geometry optimization of one-dimensional molecules at the full-CI level on a quantum computer. Results of numerical quantum circuit simulations of the geometry optimization of the H2 molecule with the STO-3G and 6-31G basis sets, the LiH and BeH2 molecules at the full-CI/STO-3G level, and the N2 molecule at the CASCI(6e,6o)/6-311G* level are given.
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Affiliation(s)
- Kenji Sugisaki
- Department
of Chemistry, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka558-8585, Japan
- JSTPRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
- Centre
for Quantum Engineering, Research and Education (CQuERE), TCG Centres for Research and Education in Science
and Technology (TCG CREST), Sector V,
Salt Lake, Kolkata700091, India
| | - Hiroyuki Wakimoto
- Department
of Chemistry, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka558-8585, Japan
| | - Kazuo Toyota
- Department
of Chemistry, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka558-8585, Japan
| | - Kazunobu Sato
- Department
of Chemistry, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka558-8585, Japan
| | - Daisuke Shiomi
- Department
of Chemistry, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka558-8585, Japan
| | - Takeji Takui
- Department
of Chemistry, Graduate School of Science, Osaka Metropolitan University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka558-8585, Japan
- Research
Support Department/University Research Administrator Center, University
Administration Division, Osaka Metropolitan
University, 3-3-138 Sugimoto,
Sumiyoshi-ku, Osaka558-8585, Japan
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Benavides-Riveros CL, Chen L, Schilling C, Mantilla S, Pittalis S. Excitations of Quantum Many-Body Systems via Purified Ensembles: A Unitary-Coupled-Cluster-Based Approach. PHYSICAL REVIEW LETTERS 2022; 129:066401. [PMID: 36018631 DOI: 10.1103/physrevlett.129.066401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 07/13/2022] [Indexed: 06/15/2023]
Abstract
State-average calculations based on a mixture of states are increasingly being exploited across chemistry and physics as versatile procedures for addressing excitations of quantum many-body systems. If not too many states should need to be addressed, calculations performed on individual states are also a common option. Here we show how the two approaches can be merged into one method, dealing with a generalized yet single pure state. Implications in electronic structure calculations are discussed and for quantum computations are pointed out.
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Affiliation(s)
- Carlos L Benavides-Riveros
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- INO-CNR BEC Center, I-38123 Trento, Italy
| | - Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Christian Schilling
- Faculty of Physics, Arnold Sommerfeld Centre for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Sebastián Mantilla
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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