Effects of control error on an adiabatic quantum algorithm

Abstract

Noise in adiabatic quantum computation can be modelled as a perturbation of the problem Hamiltonian. For a type of noise called control error, the perturbation can be considered to have the same structure as the problem Hamiltonian. If the problem Hamiltonian, and therefore the noise, are 2-local, then the result of the adiabatic algorithm can be simulated somewhat more efficiently than an algorithm with an arbitrary problem Hamiltonain. Using optimized numerical methods, I present an analysis of the effect of 1-local and 2-local control error on the success of an adiabatic algorithm that solves the agree problem. Furthermore, I examine how the maximum allowable noise, or success threshold, scales with the number of qubits. These analyses suggest the existence of a minimum success threshold for the particular algorithm considered in the presence of only 2-local noise on an arbitrarily large number of qubits, as well as a polynomial decrease in success threshold with the number of qubits.