Tensor-Train Split-Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations

The machine learning approaches are applied in the dynamical simulation of open quantum systems. The long short-term memory recurrent neural network (LSTM-RNN) models are used to simulate the long-time quantum dynamics, which are built based on the key information of the short-time evolution. We employ various hyperparameter optimization methods, including simulated annealing, Bayesian optimization with tree-structured parzen estimator, and random search, to achieve the automatic construction and adjustment of the LSTM-RNN models. The implementation details of three hyperparameter optimization methods are examined, and among them, the simulated annealing approach is strongly recommended due to its excellent performance. The uncertainties of the machine learning models are comprehensively analyzed by the combination of bootstrap sampling and Monte Carlo dropout approaches, which give the prediction confidence of the LSTM-RNN models in the simulation of the open quantum dynamics. This work builds an effective machine learning approach to simulate the dynamics evolution of open quantum systems. In addition, the current study provides an efficient protocol to build optimal neural networks and estimate the trustiness of the machine learning models.

Section: Methodsmentioning

confidence: 99%

“…More detailed discussions on this algorithm were found in previous works. 109,110 The error minimization can be achieved by the definition of the orthogonal projection of the evolution vector onto the tangent space given by a predefined MPS manifold…”

Section: Tensor-trainmentioning

confidence: 99%

Automatic Evolution of Machine-Learning-Based Quantum Dynamics with Uncertainty Analysis

Lin¹,

Peng²,

Xu³

et al. 2022

“…However, numerically exact full-quantum methods such as numerically exact wavepacket propagation approaches , are usually only feasible to a small number of degrees of freedom (DoFs) due to the curse of dimensionality. Through decomposing the wave function of a large high-rank tensor into the product of many small low-rank tensors, the time-dependent density matrix renormalization group (TD-DMRG) − and multiconfigurational time-dependent Hartree (MCTDH) − as well as its multilayer variant (ML-MCTDH) , increased the computational efficiency remarkably and made it feasible to simulate the dynamics of excitonic systems with up to a few hundred vibrational or phonon DoFs. This promotes the full QD simulations of nonadiabatic processes in realistic molecules with up to a few tens of atoms, ranging from charge transfer − or energy transfer to singlet fission …”

Section: Introductionmentioning

confidence: 99%

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

Liu

Ma³

2023

Quantum dynamics (QD) simulation is a powerful tool for interpreting ultrafast spectroscopy experiments and unraveling their microscopic mechanism in out-of-equilibrium excited state behaviors in various chemical, biological, and material systems. Although state-of-the-art numerical QD approaches such as the time-dependent density matrix renormalization group (TD-DMRG) already greatly extended the solvable system size of general linearly coupled exciton–phonon models with up to a few hundred phonon modes, the accurate simulation of larger system sizes or strong system-environment interactions is still computationally highly challenging. Based on quantum information theory (QIT), in this work, we realize that only a small number of effective phonon modes couple to the excitonic system directly regardless of a large or even infinite number of modes in the condensed phase environment. On top of the identified small number of direct effective modes, we propose a hierarchical mapping (HM) approach through performing block Lanczos transformations on the remaining indirect modes, which transforms the Hamiltonian matrix to a nearly block-tridiagonal form and eliminates the long-range interactions. Numerical tests on model spin-boson systems and realistic singlet fission models in a rubrene crystal environment with up to 7000 modes and strong system-environment interactions indicate HM can reduce the system size by 1–2 orders of magnitude and accelerate the calculation by ∼80% without losing accuracy.

“…The developed technique has a resemblance with the methods based on the propagation of the matrix product states, tree tensor networks, and density matrix renormalization group formalism useful in different quantum chemical/dynamical applications. − These methods are formulated for the wave function of a quantum state, instead we consider here the time-evolution of the surprisal. The proposed route is highly efficient for the propagation of the states of maximal entropy (subject to constraints), providing exceedingly small number of the time-dependent coefficients for the coherent multi-electronic state dynamics. − …”

Section: Introductionmentioning

confidence: 99%

Density Matrix via Few Dominant Observables for the Ultrafast Non-Radiative Decay in Pyrazine

Komarova

2023

Unraveling the density matrix of a non-stationary quantum state as an explicit function of a few observables provides a complementary view of quantum dynamics. We have recently developed a practical way to identify the minimal set of the dominant observables that govern the quantal dynamics even in the case of strong non-adiabatic effects and large anharmonicity [Komarova et al., J. Chem. Phys. 155, 204110 (2021)]. Fast convergence in the number of the dominant contributions is achieved when instead of the density matrix we describe the time-evolution of the surprisal, the logarithm of the density operator. In the present work, we illustrate the efficiency of the proposed approach using an example of the early time dynamics in pyrazine in a Hilbert space accounting for up to four vibrational normal modes, {Q 10a, Q 6a, Q 1, and Q 9a}, and two coupled electronic states, the optically dark B 1 3 u ( n π * ) and the bright B 1 2 u ( π π * ) states. Dynamics in four-dimensional (4D) configurational space involve 19,600 vibronic eigenstates. Our results reveal that the rate of the ultrafast population decay as well as the shape of the nuclear wave packets in 2D, accounting only for {Q 10a,Q 6a} normal modes, are accurately captured with only six dominant time-independent observables in the surprisal. Extension of the dynamics to 3D and 4D vibrational subspace requires only five additional constraints. The time-evolution of a quantum state in 4D vibrational space on two electronic states is thus compacted to only 11 time-dependent coefficients of these observables.