Quantum Inf Process (2015) 14:3739–3755
Noncyclic geometric quantum computation
and preservation of entanglement for a
two-qubit Ising model
H. Rangani Jahromi
· M. Amniat-Talab
Received: 30 April 2015 / Accepted: 27 July 2015 / Published online: 7 August 2015
© Springer Science+Business Media New York 2015
Abstract After presenting an exact analytical solution of time-dependent Schrödinger
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 inves-
tigate how the entanglement can be controlled by changing the external parameters.
Because of the important role of maximally entangled Bell states in quantum com-
munication, 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 angu-
lar 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.
H. Rangani Jahromi
Physics Department, Faculty of Sciences, Urmia University, P.B. 165, Urmia, Iran