Testing quantum adiabaticity with quench echo

Adiabaticity of quantum evolution is important in many settings. One example is the adiabatic quantum computation. Nevertheless, up to now, there is no effective method to test the adiabaticity of the evolution when the eigenenergies of the driven Hamiltonian are not known. We propose a simple method to check adiabaticity of a quantum process for an arbitrary quantum system. We further propose a operational method for finding a uniformly adiabatic quench scheme based on Kibble-Zurek mechanism for the case when the initial and the final Hamiltonians are given. This method should help in implementing adiabatic quantum computation.Comment: This is a new version. Some typos in the New Journal of Physics version have been correcte