Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics

Greene, Samuel M.; Batista, Víctor S.

doi:10.1021/acs.jctc.7b00608

Cited by 100 publications

(105 citation statements)

References 51 publications

(104 reference statements)

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“…Chemical quantum dynamics is another important target for quantum simulation [91][92][93][94][95]. This field is concerned with modeling time-dependent electronic and nuclear quantum effects in molecules (as distinct from computing the time-independent electronic or nuclear eigenstates in quantum chemistry and quantum molecular spectroscopy).…”

Section: Chemical Quantum Dynamicsmentioning

confidence: 99%

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

et al. 2020

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As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman’s idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.

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Section: Chemical Quantum Dynamicsmentioning

confidence: 99%

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

et al. 2020

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“…Certainly, the effective potential given in Eq. (14) defines the nuclear motion in the very beginning of the dynamics. Because both two action variables were obtained stochastically by sampling procedure, the effective potential is the linear combination of the S0 and S1 potential.…”

Section: Azomethanementioning

confidence: 99%

On-the-fly Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

Xie²,

Peng³

et al. 2021

Preprint

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The ‘on-the-fly’ version of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (SQC/MM) is implemented to study the nonadiabatic dynamics at conical intersections of polyatomic systems. The current ‘on-the-fly’ implementation of the SQC/MM method is based on the adiabatic representation and the dressed momentum. To include the zero-point energy (ZPE) correction of the electronic mapping variables, we employed both the γ-adjusted and γ-fixed approaches. Nonadiabatic dynamics of the methaniminium cation (CH2NH2+) and azomethane are simulated using the on-the-fly SQC/MM method. For CH2NH2+, both two ZPE correction approaches give reasonable and consistent results. However, for azomethane, the γ-adjusted version of the SQC/MM dynamics behaves much better than the γ-fixed version. The further analysis indicates that it is always recommended to use the γ-adjusted SQC/MM dynamics in the on-the-fly simulation of photoinduced dynamics of polyatomic systems, particularly when the excited-state is well separated from the ground state in the Frank-Condon region. This work indicates that the on-the-fly SQC/MM method is a powerful simulation protocol to deal with the nonadiabatic dynamics of realistic polyatomic systems.

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“…To compute the time-dependent reduced density matrix ρ jj (t) in Eqn. 19 we propose the following NRPMD population expression…”

Section: B Excited States Non-adiabatic Dynamics With Nrpmdmentioning

confidence: 99%

State dependent ring polymer molecular dynamics for investigating excited nonadiabatic dynamics

Chowdhury

Huo

2019

The Journal of Chemical Physics

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Recently proposed non-adiabatic ring polymer molecular dynamics (NRPMD) approach has shown to provide accurate quantum dynamics by incorporating explicit electronic state descriptions and nuclear quantizations. Here, we present a rigorous derivation of the NRPMD Hamiltonian and investigate its performance on simulating excited state non-adiabatic dynamics. Our derivation is based on the Meyer-Miller-Stock-Thoss (MMST) mapping representation for electronic states and the ring-polymer path-integral description for nuclei, resulting in the same Hamiltonian proposed in the original NRPMD approach. In addition, we investigate the accuracy of using NRPMD to simulate photoinduced non-adiabatic dynamics in simple model systems. These model calculations suggest that NRPMD can alleviate the zero-point energy leakage problem that is commonly encountered in the classical Wigner dynamics, and provide accurate excited states non-adiabatic dynamics. This work provides a solid theoretical foundation of the promising NRPMD Hamiltonian and demonstrates the possibility of using state-dependent RPMD approach to accurately simulate electronic nonadiabatic dynamics while explicitly quantize nuclei.

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Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics

Cited by 100 publications

References 51 publications

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

On-the-fly Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

State dependent ring polymer molecular dynamics for investigating excited nonadiabatic dynamics

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