由各向异性海森伯自旋环链组成的量子位及其一位通用量子逻辑门

【作者】 严晓波；

【导师】 王顺金；

【作者基本信息】 四川大学 ， 理论物理， 2006， 硕士

【摘要】 量子状态的变化可以用量子计算的语言来描述。类似于经典计算机是由包含连线和逻辑门的线路建造的，量子计算机是由包含连线和基本量子门排列起来，形成的处理量子信息的量子线路建造的。 量子门包括单量子比特门和多量子比特门，量子门中最重要的就是受控非门和单量子比特门，因为任意的多量子比特门都可由受控非门和单量子比特门复合而成。现在有一些实现量子门的方案，比如简单谐振子、腔量子电动力学、离子阱、分子核磁共振、量子点及某些其他物理系统。 本文研究了各向异性耦合的三粒子海森伯自旋环链团簇在随时间变化的磁场中的运动。该系统的哈密顿量具有SU(2)代数结构。用代数动力学方法对此系统进行求解，得到了严格的解析解。基于严格解，可以构造一位量子逻辑门。通过调节磁场强度和频率，可以控制该量子逻辑门，实现一位量子逻辑门的任何操作。并且可以实现标准的一位通用量子逻辑门。更多还原

【Abstract】 Changes occurring to a quantum state can be described using the language of quantum computation. Analogous to the way a classical computer is built from an electrical circuit containing wires and logic gates, a quantum computer is built from a quantum circuit containing wires and elementary quantum gates to carry around and manipulate the quantum information.Qubit gates include single qubit gates and multiple qubit gates. The important ones of the qubit gates are single qubit gates and the controlled-NOT gate because of the following remarkable universality result: Any multiple qubit logic gate may be composed from controlled-NOT gate and single qubit gates. Now there are some schemes for implementation of qubit gate, for example, the simple harmonic oscillator, cavity quantum electrodynamics devices、ion traps、nuclear magnetic resonance with molecules、quantum dots and some other physical systems.We investigate an annular spin cluster made of three particles with an isotropic Heisenberg-chain controlled by a time-dependent magnetic field. The system has an SU(2) algebraic structure. Using algebraic dynamical method, we have obtained the exact analytical solution to the time dependent Schro|¨dinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and consequently the six special single qubit logic gates can be realized.更多还原