On the quantum adiabatic evolution with the most general system Hamiltonian

Abstract

In this paper, we study the problem that when quantum adiabatic evolution with the most general form of system Hamiltonian will get failed. Here the most general form means that the initial and final Hamiltonians are just designed according to the adiabatic theorem in quantum mechanics. As we will see, even in this most general model of quantum adiabatic evolution, it still exists the possibility that the quantum adiabatic computation can fail totally if some condition is satisfied, which implies the time complexity of the quantum algorithm is infinity. That is, here we propose a rather general criterion for judging whether a quantum adiabatic evolution is successful. This result largely extends the authors’ previous research on this topic, and it may be seen as a further important clue for us when designing quantum algorithms in the framework of adiabatic evolution for some practical problems.