量子系统噪声的动力学抑制

发布时间：2018-06-22 13:16

本文选题：量子控制 + 核磁共振　；参考：《清华大学》2016年博士论文

【摘要】：对量子系统实现精准操控是量子信息处理中的重要环节,而实现这一目标面临诸多难题。首先,量子系统会与环境发生耦合,导致系统出现退相干现象;其次,控制操作本身会存在各种误差,使量子系统演化偏离目标演化。目前用于实现量子精准操控的技术主要分为两类:闭环量子控制与开环量子控制。开环量子控制技术通过对量子系统引入外部控制操作来调制系统哈密顿量,使系统有效哈密顿量的演化趋近于目标演化。在这个过程中我们不必测量系统量子态和获知噪声环境的信息。本文围绕开环量子控制中的三个重要技术:滤波函数、动力学解耦以及组合脉冲,在核磁共振量子系统中开展了以下研究:一、动力学解耦技术可以延长量子态的相干时间,解耦序列可以看作在频域内对特定噪声的高通滤波器。我们研究了包含两种脉冲的复杂动力学解耦序列的滤波函数,给出了其在布洛赫球空间中的三维表示。借助滤波函数,我们讨论了三种序列针对纵向弛豫噪声和横向弛豫噪声的解耦能力差异,指出在使用脉冲资源相同的情况下,解耦序列的表现为序列结构和特定脉冲数目两种因素相互竞争的结果。二、我们在核磁共振系统中验证了复杂动力学解耦序列在混合噪声环境中的解耦表现,第一次在实验中观测到二次解耦序列的解耦优势。为了得到具有纵向弛豫和横向弛豫效应的噪声环境,我们完善了噪声模拟理论体系,首次提出利用控制场同时模拟两种弛豫效应的方法。计算解耦序列的滤波函数可以得出该序列在噪声环境中的演化保真度,实验结果精准的符合了滤波函数的理论预测。三、我们在核磁共振系统中验证了级联组合脉冲在两种时变误差同时存在时的鲁棒性表现。这些原本用于消除静态或准静态误差的组合脉冲,被证明在动态非马尔科夫噪声环境中同样具有鲁棒性,而级联组合脉冲可以同时消除原始脉冲中存在的脉冲长度误差和脉冲失谐误差。通过计算级联组合脉冲的滤波函数,我们能够得到该组合脉冲对两种误差抑制能力的差异,并找到脉冲能保持鲁棒性的噪声截止频率阈值。我们在实验中证实了级联组合脉冲的解耦表现,实验数据和滤波函数预测一致。
[Abstract]:Accurate manipulation of quantum systems is an important part of quantum information processing. First, the quantum system will be coupled with the environment, resulting in the system decoherence; secondly, there will be a variety of errors in the control operation itself, which makes the evolution of the quantum system deviate from the target evolution. At present, there are two kinds of quantum control techniques: closed loop quantum control and open loop quantum control. The open-loop quantum control technology modulates the Hamiltonian by introducing external control operations to the quantum system, which makes the evolution of the effective Hamiltonian approach to the target evolution. In this process, we do not have to measure the quantum state of the system and get information about the noise environment. This paper focuses on three important techniques in open-loop quantum control: filtering function, dynamic decoupling and combinatorial pulses. The following studies have been carried out in the NMR quantum system: firstly, the dynamic decoupling technique can prolong the coherent time of quantum states. Decoupling sequences can be regarded as high-pass filters for certain noises in frequency domain. In this paper, we study the filtering function of complex dynamical decoupling sequences containing two impulses, and give their three dimensional representation in Bloch sphere space. With the help of filtering function, we discuss the decoupling ability of three sequences for longitudinal relaxation noise and transverse relaxation noise, and point out that when the pulse resource is the same, Decoupling sequences are represented by competing results of sequence structure and number of specific pulses. Secondly, we have verified the decoupling performance of the complex dynamic decoupling sequences in the nuclear magnetic resonance system. The decoupling advantages of the quadratic decoupling sequences have been observed in experiments for the first time. In order to obtain the noise environment with longitudinal and transverse relaxation effects, we have perfected the theoretical system of noise simulation and proposed for the first time a method to simulate the two relaxation effects simultaneously by using the control field. The evolution fidelity of the decoupled sequence in noise environment can be obtained by calculating the filtering function of the decoupled sequence. The experimental results are accurate in line with the theoretical prediction of the filtering function. Thirdly, we verify the robustness of the cascaded combined pulses in the presence of two time-varying errors in the nuclear magnetic resonance (NMR) system. These combined pulses, which were originally used to eliminate static or quasi-static errors, have been proved to be equally robust in dynamic non-Markov noise environments. The cascade combined pulse can eliminate both the pulse length error and the detuning error in the original pulse at the same time. By calculating the filtering function of the cascaded combined pulse, we can obtain the difference of the combined pulse's ability to suppress the two kinds of errors, and find the threshold of the noise cutoff frequency which can keep the robustness of the pulse. We have verified the decoupling performance of cascaded combined pulses in experiments, and the experimental data are consistent with the filter function prediction.
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413

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