Effects of Errors in the Hamiltonian Programming Process of Adiabatic Quantum Computing

Abstract

In order to measure the effects of the errors we measure of the likelihood an erroneous instance of a Hamiltonian shares the same ground state as the intended Hamiltonian (resilience). The effects of errors on the spectrum of the instantaneous Hamiltonian through the evolution of the system is studied through the instantaneous gap as well as the minimum. For this work a simplistic model is used. An Ising Spin Glass to model the adiabatic quantum computer. The structure of the computers spins and allowable couplings are taken to be in accordance with the D-Wave architecture. The errors are modelled with Gaussian distributions. The model allowed for a simple scaling relation to be extracted for resilience. It was observed that resilience drops quickly as system size grows; although, computational complexity limited the study of larger systems. A minimal effect on the evolution process itself was observed through the simulations.