Algebraic Dynamics With A Quantum Logic Gate,

In quantum computation, quantum logic gates are basic elements and play a key role so that they are studied by many people. We investigate the following two systems.(1)A particle with spin-1/2 moving in a time-dependent magnetic field. (2)An anti-ferromagnetic Heisenberg chain with odd spin-1/2 particlesin time-dependent magnetic field.Both systems have an SU(2) algebraic structure. Using algebraic dynamical method, we have obtained the exact analytical solutions to the time dependent Schroedinger equations. Based on the analytical solutions, we have realized the universal single qubit logic gate controlled by the amplitude and frequency of the magnetic fields and the six special single qubit gates are realized as well. The qubit gates realized by the system(l), is called a single particle- qubit gates, whose global phase is different from standard single qubit logic gate. In order to generate the global phase , a magnetic impulse is used. The qubit gates realized by the system (2), is called spin cluster-qubit gates, controlled by the anti-ferromagnetic coupling constant and time duration, is the same with standard single qubit logic gate. The influence of environment has been discussed here. The spin cluster as a qubit is expected to be robust against the dissipation of the radiation fields compared to one spin particle case.