Consistency of the Adiabatic Theorem

TL;DR

This paper clarifies the conditions under which the adiabatic theorem holds in quantum mechanics, showing violations are due to resonant transitions, and discusses implications for adiabatic quantum computing.

Contribution

It demonstrates that violations of the adiabatic theorem are caused by resonant transitions, reaffirming the theorem's validity under certain conditions, and discusses implications for quantum computation.

Findings

Violations are due to resonant transitions between energy levels.

Traditional adiabatic theorem holds without fast driven oscillations.

Implications for adiabatic quantum computation are discussed.

Abstract

The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. In the absence of fast driven oscillations the traditional adiabatic theorem holds. Implications for adiabatic quantum computation is discussed.