Quantum Computation In A Magnetic Field Gradient And Quantum Simulation Of The One-dimension Dirac Equation Based On Trapped Ions

There are great application prospect and scientific research potential in the field of quantum computation and quantum simulation. Many efforts have been made on this field and plenty of excellent jobs have been achieved. Among the candidate systems for quantum computation and simulation, ion trap attracts people's attention because of its convenience to manipulate a single qubit and to exchange information between qubits, as well as its independence of environment. In this dissertation we propose an effective scheme of quantum computation based on trapped ions with gradient magnetic field, and discuss the relation of parity with Zitterbewegung(ZB) based on quantum simulation of Dirac equation with trapped ions. The main contents are as follows:? Based on the strong magnetic field with large gradient, we present the scheme to manipulate and store quantum information with both electric and nu-clear spins, and to implement two-qubit quantum gates with J coupling between different ions, which is induced by the gradient of the field. We discuss the fi-delity of high field approximation that is used in the scheme, showing that in the strong field (larger than 1T) this approximation works well. We also pro-pose suppressing the unwanted J coupling between different ions by polarizing passive ions, which simplifies the computational scheme a lot. An analysis about experimental feasibility of this scheme is also made.? We present the scheme to simulate Dirac equation and to observe the Zetterbewegung with a single trapped ion. We discuss the role of parity operator and propose that ZB is caused not only by the mixture of positive and nega-tive energy states, but also by the mixture of odd and even parity states. We also show that a similar role is played by the parity operator for the trapped ion in Fock-state representation and the space-inversion operator for a realistic relativistic electron. Although the ZB effect is invisible in a relativistic electron, preparation of the trapped ion in different parity states is a sophisticated job, which makes it possible to observe the parity-relevant ZB effects with currently available techniques.