Adiabatic Quantum Search in Open Systems

Abstract

Adiabatic quantum algorithms represent a promising approach to universal quantum computation. Whilst in a closed system these algorithms are limited by avoided level crossings, where the gap becomes exponentially small in the system size, their robustness in open systems remains unresolved. We study the dynamics in the proximity of such an avoided level crossing associated with the adiabatic quantum search algorithm in a quantum system that is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. At finite temperature, however, scattering processes render the algorithm inefficient and no quantum speedup can be achieved. Owing to the generic nature of our model, we expect our results to be widely applicable to other adiabatic quantum algorithms.