Geometric Quantum Computing And Spintronics

Recently, the research of the geometric quantum computing has gradually become a hot task. To be useful, quantum computers will require long decoherence time and low error rate. Any quantum computing has to solve the problems including the fault-tolerant features, decoherence and how to prepare high fidelity quantum-gate. Some papers brought forward all kinds of schemes that implemented quanta-gate geometry quanta compute project by geometry phase simplicity. The basic theme is due to the fact that geometric phases depend only on some global geometric properties, independent of the velocity of evolvement. The geometric quantum-gate is expected to be the high fidelity quantum-gate, while the high fidelity quantum-gate is no doubt important for improving tolerate error capability of the quantum computation.However, there still exist quite many disputes on whether the geometry quanta-gate has special ability against the fluctuation. It is shown by the paper that compared with the Berry geometry phase, the distortion of the geometry phase is less than dynamics one. Their results show that the Berry geometry phase is not sensitive to the fluctuation. As to the non-adiabatic quantum compute scheme that has abolished the adiabatic approximation, the paper thinks that the non-adiabatic A-A geometry phase has no special ability against the fluctuation.This article concerns the ability of the quantum-gate against the external field fluctuation while neglects decoherence time etc. The random fluctuation is used to investigate the fidelity of the geometry quanta-gate. The numerical result shows that, no matter the Berry geometry phase or the AA geometry phase has the same ability against the stochastic fluctuations as their corresponding dynamics phases, the value which removes the dynamics phase to carry out the geometry quanta-compute scheme is oppugned by this result.This article also obtains the solution of the Rashba Hamiltonian with the influences of impurity scattering. We found that in some important conclusion obtained in some previously papers about the intrinsic spin are actually incorrect. The spin of the direction of z is convergence and it is different from the result bring forward by Sinova.