Simulation of the Fermi-Hubbard model with shortcuts to adiabaticity

Abstract

This thesis investigates the efficiency of the adiabatic evolution, in the context of a 1-dimensional Fermi-Hubbard system. Two equivalent methods were used: CNOTs and FSWAPs. As it is easier to write a generalised code for CNOTs, it was the method used in subsequent sections. The sources of error in quantum simulations were studied (the adiabatic and Trotteritzation errors), and it was verified that they behaved as predicted (in particular, the adiabatic error increased with a small N, and the Trotteritzation error increased with a larger δt). The optimal parameters needed to achieve the desired infidelity were also determined. Shortcuts to adiabaticity using the Counter-Diabatic Driving method are also applied, resulting in a faster evolution