金刚石氮—空位中心自旋量子调控的理论研究

发布时间：2018-04-04 23:08

本文选题：NV中心　切入点：量子比特　出处：《中国科学院大学(中国科学院物理研究所)》2017年博士论文

【摘要】：本论文主要研究了如何对金刚石中NV中心自旋进行有效的量子调控及操控过程中几何相位的变化。首先,我简单介绍了量子信息的发展史,量子计算的基本要素量子比特和量子逻辑门,然后又列举了现今可用来实现量子计算的若干方法,最后引出了我们论文主要的研究对象NV中心自旋,并且简要回顾了NV中心自旋调控的研究历史。一般地,在S_z表象下,可以把二能级系统写成一个简单的2×2矩阵。但是也可以采用逆向思维,即考虑若想实现目标态,到底需要何种脉冲才能实现。这样的思考方式非常适合处理量子调控的相关问题,最后精确求解得到时间演化算符,它是这一问题的核心。这些方法构造得到的脉冲不但局域性好,而且能够保证逻辑门操作具有很高的保真度。在本论文中,我们精确求解了单个NV中心自旋在一类特殊的含时磁场中,如何演化的过程。至关重要的一点,便是引入了对称态(?)和反对称态(?),进而把一个看似复杂的三能级问题,化成了一个二能级问题。然后基于二能级精确解的办法,经过幺正变换,可以精确求解得到三能级系统的时间演化算符。通过该算符,我们可以很容易地在NV中心自旋体系中实现态的制备和量子逻辑门的操作。而且,我们还用Lindblad主方程的办法考察了耗散和磁场的涨落对该体系演化的影响。计算结果表明,该方法在逻辑门的操作中同样能够保证很高的保真度。另外,我们还利用另外一种方法去求解这一含时的问题。该方法的思路更加清晰,所引入的含时参量需要满足的约束条件更少,使得它们更容易构造。通过引入简单的初等函数,便可得到在初始时刻和终点时刻磁场强度均为0的解,并同样能够在纳秒量级内实现量子逻辑门的操作。利用该方法,我们还解析求解了演化过程中的非绝热几何相位。计算结果表明,它正好是态矢量在布洛赫球上的轨迹所形成的立体角的一半。
[Abstract]:In this paper, we mainly study how to control the NV center spin effectively and how to change the geometric phase in the process of manipulation.First of all, I briefly introduce the history of quantum information, the basic elements of quantum computing, quantum bits and quantum logic gates, and then list some methods that can be used to realize quantum computing.Finally, the main research object of this paper is NV center spin, and the history of NV center spin regulation is briefly reviewed.In general, the two-level system can be written into a simple 2 脳 2 matrix under the SZ representation.However, reverse thinking can also be used, that is to say, what kind of pulse is needed to achieve the target state.This way of thinking is very suitable for dealing with the related problems of quantum regulation. Finally, the time evolution operator is obtained by exact solution, which is the core of this problem.The pulses constructed by these methods not only have good locality, but also can guarantee the high fidelity of logic gate operation.In this paper, we accurately solve the evolution of a single NV center spin in a special time-dependent magnetic field.The most important point is the introduction of a symmetric state.And antisymmetric states, thus turning a seemingly complex three-level problem into a two-level problem.Then, based on the method of two-level exact solution and unitary transformation, the time evolution operator of three-level system can be solved accurately.By using this operator, we can easily realize the preparation of states and the operation of quantum logic gates in the NV central spin system.Furthermore, the effects of dissipation and magnetic field fluctuations on the evolution of the system are investigated by means of the Lindblad master equation.The calculation results show that the method can also guarantee high fidelity in the operation of logic gates.In addition, we use another method to solve this time-dependent problem.The idea of this method is clearer and the time-dependent parameters need to satisfy fewer constraints which make them easier to construct.By introducing a simple elementary function, we can get the solution that the magnetic field intensity is 0 at the beginning and the end point, and can also realize the operation of the quantum logic gate in the nanosecond order of magnitude.Using this method, we also analytically solve the non-adiabatic geometric phase in the evolution process.The calculated results show that it is exactly half of the solid angle formed by the trajectory of the state vector on the Bloch sphere.
【学位授予单位】：中国科学院大学(中国科学院物理研究所)
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O413

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