Trace preserving quantum dynamics using a novel reparametrization-neutral summation-by-parts difference operator

We describe a method for performing nuclear quantum dynamics calculations using standard, grid-based algorithms, including the multiconfiguration time-dependent Hartree (MCTDH) method, where the potential energy surface (PES) is calculated "on-the-fly". The method of Gaussian process regression (GPR) is used to construct a global representation of the PES using values of the energy at points distributed in molecular configuration space during the course of the wavepacket propagation. We demonstrate this direct dynamics approach for both an analytical PES function describing 3-dimensional proton transfer dynamics in malonaldehyde and for 2- and 6-dimensional quantum dynamics simulations of proton transfer in salicylaldimine. In the case of salicylaldimine we also perform calculations in which the PES is constructed using Hartree-Fock calculations through an interface to an ab initio electronic structure code. In all cases, the results of the quantum dynamics simulations are in excellent agreement with previous simulations of both systems yet do not require prior fitting of a PES at any stage. Our approach (implemented in a development version of the Quantics package) opens a route to performing accurate quantum dynamics simulations via wave function propagation of many-dimensional molecular systems in a direct and efficient manner.

In the present work, we suggest an approach for describing dynamics of finite-dimensional quantum systems in terms of pseudostochastic maps acting on probability distributions, which are obtained via minimal informationally complete quantum measurements. The suggested method for probability representation of quantum dynamics preserves the tensor product structure, which makes it favourable for the analysis of multi-qubit systems. A key advantage of the suggested approach is that minimal informationally complete positive operator-valued measures (MIC-POVMs) are easier to construct in comparison with their symmetric versions (SIC-POVMs). We establish a correspondence between the standard quantum-mechanical formalism and the MIC-POVM-based probability formalism. Within the latter approach, we derive equations for the unitary von-Neumann evolution and the Markovian dissipative evolution, which is governed by the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) generator. We apply the MIC-POVM-based probability representation to the digital quantum computing model. In particular, for the case of spin-1/2 evolution, we demonstrate identifying a transition of a dissipative quantum dynamics to a completely classical-like stochastic dynamics. One of the most important findings is that the MIC-POVM-based probability representation gives more strict requirements for revealing the non-classical character of dissipative quantum dynamics in comparison with the SIC-POVM-based approach. Our results give a physical interpretation of quantum computations and pave a way for exploring the resources of noisy intermediate-scale quantum devices.

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein-Tavis-Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

In recent years, quantum walks have been proposed as promising resources for the simulation of physical quantum systems. In fact it is widely adopted to simulate quantum dynamics. Up to now single particle quantum walks have been experimentally demonstrated by different approaches, while only few experiments involving many-particle quantum walks have been realized. Here we simulate the 2-particle dynamics on a discrete time quantum walk, built on an array of integrated waveguide beam splitters. The polarization independence of the quantum walk circuit allowed us to exploit the polarization entanglement to encode the symmetry of the two-photon wavefunction, thus the bunching-antibunching behavior of non interacting bosons and fermions has been simulated. We have also characterized the possible distinguishability and decoherence effects arising in such a structure. This study is necessary in view of the realization of a quantum simulator based on an integrated optical array built on a large number of beam splitters.

In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric phases in the evolution of the density matrix. It is shown that such geometric phases must also be considered in the quantum-classical Liouville equation for a classical bath with canonical phase space coordinates; this occurs whenever the adiabatics basis is complex (as in the case of a magnetic field coupled to the quantum subsystem). When the quantum subsystem is weakly coupled to the spin environment, non-adiabatic transitions can be neglected and one can construct an effective non-Markovian computer simulation scheme for open quantum system dynamics in classical spin environments. In order to tackle this case, integration algorithms based on the symmetric Trotter factorization of the classical-like spin propagator are derived. Such algorithms are applied to a model comprising a quantum two-level system coupled to a single classical spin in an external magnetic field. Starting from an excited state, the population difference and the coherences of this two-state model are simulated in time while the dynamics of the classical spin is monitored in detail. It is the author's opinion that the numerical evidence provided in this paper is a first step toward developing the simulation of quantum dynamics in classical spin environments into an effective tool. In turn, the ability to simulate such a dynamics can have a positive impact on various fields, among which, for example, nano-science.

Harnessing a static magnetic field to drive molecular vibrations presents a promising avenue for controlling chemical processes. However, the coupling of nuclear dynamics with an external magnetic field has largely been explored only through classical approximations. In this work, we introduce a time-dependent quantum dynamics formalism based on London nuclear-electronic orbitals, enabling the simulation of magnetic field-driven quantum dynamics. Through simulations of HCN and H2CO molecules, we provide a detailed analysis of how the relative orientation of the magnetic field and vibrational symmetry influence the resulting quantum dynamics. Our findings reveal field-induced mode couplings and symmetry-dependent effects, offering new insights into the role of magnetic fields in vibrational control. This work establishes a quantum mechanical framework for understanding and manipulating vibrational dynamics using external magnetic fields, paving the way for novel applications in spectroscopy, reaction dynamics, and quantum control.

The simulations of spectroscopy and quantum dynamics are of vital importance to the understanding of the electronic processes in complex systems, including the radiative/radiationless electronic relaxation relevant for optical emission, charge/energy transfer in molecular aggregates related to carrier mobility in organic materials, as well as photovoltaic and thermoelectric conversion, light‐harvesting and spin transport, and so forth. In recent years, time‐dependent density matrix renormalization group (TD‐DMRG) has emerged as a general, numerically accurate and efficient method for high‐dimensional full‐quantum dynamics. This review will cover the fundamental algorithms of TD‐DMRG in the modern framework of matrix product states (MPS) and matrix product operators (MPO), including the basic algebra with respect to MPS and MPO, the novel time evolution schemes to propagate MPS, and the automated MPO construction algorithm to encode generic Hamiltonian. Most importantly, the proposed method can handle the mixed state density matrix at finite temperature, enabling quantum statistical description for molecular aggregates. We demonstrate the performance of TD‐DMRG by benchmarking with the current state‐of‐the‐art methods for simulating quantum dynamics of the spin‐boson model and the Frenkel–Holstein(–Peierls) model. As applications of TD‐DMRG to real‐world problems, we present theoretical investigations of carrier mobility and spectral function of rubrene crystal, and the radiationless decay rate of azulene with an anharmonic potential energy surface.This article is categorized under: Theoretical and Physical Chemistry > Statistical Mechanics Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Software > Simulation Methods

Classical simulations of real-space quantum dynamics are challenging due to the exponential scaling of computational cost with system dimensions. Quantum computers offer the potential to simulate quantum dynamics with polynomial complexity; however, existing quantum algorithms based on the split-operator techniques require large-scale fault-tolerant quantum computers that remain elusive in the near future. Here, we present variational simulations of real-space quantum dynamics suitable for implementation in noisy intermediate-scale quantum (NISQ) devices. The Hamiltonian is first encoded onto qubits using a discrete variable representation and binary encoding scheme. We show that direct application of a real-time variational quantum algorithm based on the McLachlan's principle is inefficient as the measurement cost grows exponentially with the qubit number for general potential energy, and an extremely small time-step size is required to achieve accurate results. Motivated by the insights that many chemical dynamics occur in the low-energy subspace, we propose a subspace expansion method by projecting the total Hamiltonian, including the time-dependent driving field, onto the system low-energy eigenstate subspace using quantum computers, and the exact quantum dynamics within the subspace can then be solved classically. We show that the measurement cost of the subspace approach grows polynomially with dimensionality for general potential energy. Our numerical examples demonstrate the capability of our approach, even under intense laser fields. Our work opens the possibility of simulating chemical dynamics with NISQ hardware.

We introduce an efficient configuration interaction (CI) method for the calculation of mixed quantum and classical nonadiabatic molecular dynamics for multiple electrons. For any given realization of the classical degrees of freedom (e.g., a solvent), the method uses a novel real-space quadrature to efficiently compute the Coulomb and exchange interactions between electrons. We also introduce an approximation whereby the classical molecular dynamics is propagated for several time steps on electronic potential energy surfaces generated using only a particularly important subset of the CI basis states. By only updating the important-states subset periodically, we achieve significant reductions in the computational cost of solving the multielectron quantum problem. We test the real-space quadrature for the cases of two electrons confined in a cubic box with infinitely repulsive walls and two electrons dissolved in liquid water that occupy a single cavity, so-called hydrated dielectrons. We then demonstrate how to perform mixed quantum and classical nonadiabatic dynamics by combining these computational techniques with the mean-field with surface hopping algorithm of Prezhdo and Rossky [J. Chem. Phys. 107, 825 (1997)]. Finally, we illustrate the practicality of the approach to multielectron nonadiabatic dynamics by examining the nonadiabatic relaxation dynamics of both spin singlet and spin triplet hydrated dielectrons following excitation from the ground to the first excited state.

Steel cord conveyor belts are widely used in long-distance transportation of various materials. The steel cord belt is composed of rubber and steel cord core, exhibiting excellent viscoelasticity and complex dynamic characteristics during operation. The existing static elastic modulus cannot accurately reflect the real dynamic properties of the conveyor belt. In this paper, based on the catenary theory, the formula for the dynamic elastic modulus of the conveyor belt is derived by introducing the sag and elastic deformation of the steel cord conveyor belt on the basis of the static elastic modulus. The dynamic modeling of the steel cord conveyor belt is carried out using rigid belt block element + flexible beam method. Then, the RecurDyn software is used to establish the dynamic simulation system of the belt conveyor and conduct simulations, which are validated through a test bench. The results show that dynamics simulation based on the dynamic elastic modulus is closer to the real dynamic characteristics of the belt conveyor. Finally, the dynamic characteristics of belt conveyors under different start-up times, different start-up speeds, and idler spacing are analyzed using this modeling and simulation method. The results demonstrate that the dynamic elastic modulus can accurately reflect the real dynamic properties of the conveyor belt, providing a more accurate dynamic modeling and simulation method for the design of belt conveyors.

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.

We investigate the ecient computation of a few of the lowest eigenvalues of a symmetric eigenvalue problem occurring in quantum dynamical molecular simulations. The large sparse system of order n 3 is highly structured such that its multiplication with a vector costs O(n 3 logn) oating point operations only. We compare a number of eigensolvers: subspace iteration, two variants of the restarted Lanczos algo- rithm, among them ARPACK, the Jacobi-Davidson algorithm and the classical algorithms from LAPACK for full matrices. Some of them are applied with a shift-and-invert spectral transformation. The arising systems of equations are solved by the preconditioned conjugate gradient method for which new ecient ADI-type preconditioners are proposed and analyzed.

A straightforward algorithm is proposed for simulating and visualizing nonrelativistic quantum dynamics in terms of the collective behavior of classical particles. In this approach, a quantum particle is treated as a swarm (collection) of its classical samples interacting with one another by simple rules involving the emission and absorption of associated photons. The quantum dynamics is regarded as resulting from the collective behavior of the swarm, and the eigenstates are treated as equilibrium states of the process of photon emission and absorption. Entanglement is seen as classical correlation between samples from distinct swarms; the information on this correlation is stored in a spatiotemporal section of the model inaccessible to the user. Amplitudes are invariably treated as consisting of amplitude quanta. A Coulomb field experienced by quantum particles is represented in a similar manner to the free spreading of a wave packet, by point interaction between the particle samples and the samples of scalar photons propagating by diffusion. This provides a square-root gam in computational speed against the direct method involving item-by-item examination. The approach presented covers decoherence and allows natural generalization to multiparticle quantum electrodynamics, the amount of memory required growing linearly.

Singlet fission is a photophysical process in organic molecules that generates two triplet electronic states from an excited singlet electronic state. Molecules exhibiting singlet fission can multiply charge carriers and thus have the potential to enhance the performance of solar cells beyond the Shockley-Queisser limit by reducing thermalization losses. However, in order to implement singlet fission for applications in photovoltaics, it is essential to understand how charge or energy can be harvested from triplet excitons. In this work, we investigate these processes in a prototypical donor-acceptor complex consisting of a bis(diazadiborine)-based chromophore as a singlet fission-active donor and tetracyanoquinodimethane as an acceptor molecule. Using a combined approach of high-level ab initio multireference perturbation theory techniques and quantum dynamical simulations, we show the existence of intermolecular singlet fission, charge and energy transfer following intramolecular singlet fission, and energy loss decay channels to low-lying states as the three competing charge and energy transfer mechanisms from the donor to the acceptor molecule. We analyze the role of the different electronic states, specific vibrational modes, and vibronic couplings in these processes. The results provide insights into the rational design of donor-acceptor systems with efficient singlet fission-based charge and energy transfer.

The Ehrenfest with collapse-to-a-block (TAB) molecular dynamics approach was recently introduced to allow accurate simulation of nonadiabatic dynamics on many electronic states. Previous benchmarking work has demonstrated it to be highly accurate for modelling dynamics in one-dimensional analytical models, but nonadiabatic dynamics often involves conical intersections, which are inherently two-dimensional. In this report, we assess the performance of TAB on two-dimensional models of cascades of conical intersections in dense manifolds of states. Several variants of TAB are considered, including TAB-w, which is based on the assumption of a Gaussian rather than exponential decay of the coherence, and TAB-DMS, which incorporates an efficient collapse procedure based on approximate eigenstates. Upon comparison to numerically exact quantum dynamics simulations, it is found that all TAB variants provide a suitable description of the dynamical passage through a cascade of conical intersections. The TAB-w approach is found to provide a somewhat more accurate description of population dynamics than the original TAB method, with final absolute population errors ≤ 0.013 in all cases. Even when only four approximate eigenstates are computed, the use of approximate eigenstates was found to introduce minimal additional error (absolute population error ≤ 0.018 in all models).