Noncyclic geometric quantum computation and preservation of entanglement for a two-qubit Ising model

Abstract

After presenting an exact analytical solution of time-dependent Schrodinger equation, we study the dynamics of entanglement for a two-qubit Ising model. One of the spin qubits is driven by a static magnetic field applied in the direction of the Ising interaction, while the other is coupled with a rotating magnetic field. We also investigate how the entanglement can be controlled by changing the external parameters. Because of the important role of maximally entangled Bell states in quantum communication, we focus on the generalized Bell states as the initial states of the system. It is found that the entanglement evolution is independent of the initial Bell states. Moreover, we can preserve the initial maximal entanglement by adjusting the angular frequency of the rotating field or controlling the exchange coupling between spin qubits. Besides, our calculation shows that the entanglement dynamics is unaffected by the static magnetic field imposed in the direction of the Ising interaction. This is an interesting result, because, as we shall show below, this driving field can be used to control and manipulate the noncyclic geometric phase without affecting the system entanglement. Besides, the nonadiabatic and noncyclic geometric phase for evolved states of the present system are calculated and described in detail. In order to identify the unusable states for quantum communication, completely deviated from the initial maximally entangled states, we also study the fidelity between the initial Bell state and the evolved state of the system. Interestingly, we find that these unusable states can be detected by geometric quantum computation.