Quasi-classical mapping Hamiltonian methods have recently emerged as a promising approach for simulating electronically nonadiabatic molecular dynamics. The classicallike dynamics of the overall system within these methods makes them computationally feasible and they can be derived based on well-defined semiclassical approximations.However, the existence of a variety of different quasi-classical mapping Hamiltonian methods necessitates a systematic comparison of their respective advantages and limitations. Such a benchmark comparison is presented in this paper. The approaches compared include the Ehrenfest method, the symmetrical quasi-classical (SQC) method, and five variations of the linearized semiclassical (LSC) method, three of which employ a modified identity operator. The comparison is based on a number of popular nonadiabatic model systems; the spin-boson model, a Frenkel bi-exciton model and 1

In this work, we investigate the ability of different quasiclassical mapping Hamiltonian methods to simulate the dynamics of electronic transitions through conical intersections. The analysis is carried out within the framework of the linear vibronic coupling (LVC) model. The methods compared are the Ehrenfest method, the symmetrical quasiclassical method, and several variations of the linearized semiclassical (LSC) method, including ones that are based on the recently introduced modified representation of the identity operator. The accuracy of the various methods is tested by comparing their predictions to quantum-mechanically exact results obtained via the multiconfiguration time-dependent Hartree (MCTDH) method. The LVC model is found to be a nontrivial benchmark model that can differentiate between different approximate methods based on their accuracy better than previously used benchmark models. In the three systems studied, two of the LSC methods are found to provide the most accurate description of electronic transitions through conical intersections.

The generalized quantum master equation (GQME) provides a powerful framework for simulating electronically nonadiabatic molecular dynamics. Within this framework, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density matrix is fully captured by a memory kernel superoperator. In this paper, we consider two different procedures for calculating the memory kernel of the GQME from projection-free inputs obtained via the combination of the mapping Hamiltonian (MH) approach and the linearized semiclassical (LSC) approximation. The accuracy and feasibility of the two procedures are demonstrated on the spin-boson model. We find that although simulating the electronic dynamics by direct application of the two LSC-based procedures leads to qualitatively different results that become increasingly less accurate with increasing time, restricting their use to calculating the memory kernel leads to an accurate description of the electronic dynamics. Comparison with a previously proposed procedure for calculating the memory kernel via the Ehrenfest method reveals that MH/LSC methods produce memory kernels that are better behaved at long times and lead to more accurate electronic dynamics.

We present a quantum algorithm based on the generalized quantum master equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system–bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.