Quantum simulation of discretized harmonic oscillator

Abstract

In this work, we conduct a quantum simulation of a particle in a harmonic oscillator potential on a quantum chip provided by IBM quantum experience platform. The simulation is carried out in two spatial dimensions and the algorithm used is generalized for n-spatial dimensions. Thus, the mentioned approach can be used to simulate n-dimensional harmonic oscillator. We implement the time translation unitary operator on an arbitrary quantum state to show that the probability amplitudes of position oscillate in time. We propose a quantum circuit to effectuate the time translation operator. The proposed circuit is then generalized for a n-qubit system that can be used to realize more meticulous simulations. © 2021, Chapman University.