Efficient quantum dynamics simulations for periodic potentials

Abstract

Quantum algorithms are designed to efficiently solve many problems that are thought to be difficult classically. A specific case is the efficient simulation of time evolution of quantum systems. This work provides a general framework for such simulations and further uses symmetry of the problems to arrive at efficient quantum algorithms. These algorithms were simulated and analysed using parallel library routines developed in Python. The systems studied as a part of this work are: quantum harmonic oscillator, Bragg scattering from a periodic potential, diffusion of two-dimensional wave packets on square and graphene lattices, and quantum relativistic propagation effects in presence of potential barriers in graphene (pair production and perfect tunnelling).