“…The role of the adiabatic theorem in the study of slowly varying quantum mechanical systems spans a vast array of fields and applications, such as the Landau-Zener theory of energy level crossings in molecules [9,10], quantum field theory [11], and Berry's phase [12]. In recent years geometric phases [13] have been proposed to perform quantum information processing [14,15,16], with adiabaticity assumed in a number of schemes for geometric quantum computation (e.g., [17,18,19,20]). Additional interest in adiabatic processes has arisen in connection with the concept of adiabatic quantum computing, in which slowly varying Hamiltonians appear as a promising mechanism for the design of new quantum algorithms and even as an alternative to the conventional quantum circuit model of quantum computation [21,22,23].…”