Time dependent quantum mechanics using picosecond time steps: Application to predissociation of HeI2

Simulation of Chemical Reactions on a Quantum Computer

Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities. In this study, we develop and apply a quantum computing algorithm for the calculation of scattering matrix elements. In our approach, we employ the time-dependent method based on the Møller operator formulation where the S-matrix element between the respective reactant and product channels is determined through the time correlation function of the reactant and product Møller wavepackets. We successfully apply our quantum algorithm to calculate scattering matrix elements for 1D semi-infinite square well potential and on the colinear hydrogen exchange reaction. As we navigate the complexities of quantum interactions, this quantum algorithm is general and emerges as a promising avenue, shedding light on new possibilities for simulating chemical reactions on quantum computers.

Using preconditioned adaptive step size Runge-Kutta methods for solving the time-dependent Schrödinger equation

If the Hamiltonian is time dependent it is common to solve the time-dependent Schrödinger equation by dividing the propagation interval into slices and using an (e.g., split operator, Chebyshev, Lanczos) approximate matrix exponential within each slice. We show that a preconditioned adaptive step size Runge-Kutta method can be much more efficient. For a chirped laser pulse designed to favor the dissociation of HF the preconditioned adaptive step size Runge-Kutta method is about an order of magnitude more efficient than the time sliced method.