基于核磁共振系统的拓扑相量子模拟和拓扑量子计算实验研究

发布时间：2017-12-26 21:22

本文关键词：基于核磁共振系统的拓扑相量子模拟和拓扑量子计算实验研究　出处：《中国科学技术大学》2016年博士论文　论文类型：学位论文

【摘要】：基于量子力学原理构建的量子计算机具有经典计算机不可比拟的计算能力。然而,噪声和退相干是实现量子计算机的主要障碍之一。噪声来源于量子比特上操作的不完美；退相干起源于量子系统与环境间不可避免的相互作用。噪声和退相干会导致编码信息的部分丢失甚至完全错误。解决方案之一是量子纠错。但这需要额外引进辅助比特消耗过多的资源,而且纠错过程本身也是有噪声的。另一种策略是拓扑量子计算。与主动的量子纠错方式不同,拓扑量子计算是被动的,即无需作任何的尝试或操作让系统无噪声,因为系统本身具有鲁棒性的自纠错功能。这与系统的整体拓扑性质有关。拓扑量子计算是目前已知容错率最高的量子计算方案。拓扑量子计算方案依赖于拓扑相的存在。拓扑相是一类不能由经典朗道对称破缺理论描述的奇特的物质态。这种态具有一些有趣的性质,如依赖于拓扑流形的基态简并度,准粒子分数统计和拓扑纠缠熵等。一类特殊的拓扑物质态称为拓扑序,可描述为有能隙且具有不受微扰影响的长程纠缠模式。已知的例子是分数量子霍尔态,是首次在真实体系下观测到拓扑序。另外在一些二维晶格模型中也存在拓扑序。拓扑序不仅为容错量子计算提供了天然的无噪声介质,同时在凝聚态物理中作为基础科学研究如拓扑性质,拓扑相变以及新型材料的发现等也具有重要意义。在真实系统中观测拓扑相和实现拓扑量子计算极具挑战,主要受限于目前的实验方法和控制技术。例如,存在拓扑序的二维晶格模型常涉及多体相互作用(如toric code模型具有四体相互作用),并且构建一个晶格往往需要较多的量子比特。实验驱动和控制这样复杂的多量子比特系统不是一件容易的事情。也正因为此,拓扑量子计算的研究依然停留在理论中,无任何相关的实验报道。量子模拟用一个可控的量子系统模拟复杂的或难以观测的物理现象,在凝聚态物理,高能物理和量子化学等邻域有着许多成功的应用。量子模拟为我们提供了一个有力的手段去探索拓扑相和拓扑量子计算。另一方面,作为量子模拟的物理实现平台之一,核磁共振体系在多量子比特实验中具有成熟的控制技术和精确的测量手段,是一个很好的测试平台。本人在攻读博士学位期间基于核磁共振系统对拓扑相量子模拟和拓扑量子计算方向展开了系列理论和实验研究,主要创新性成果有：1.利用核磁共振系统对拓扑相进行了系列的量子模拟实验研究： (i)国际上首次实验实现了不同拓扑序间的绝热跃迁。实验中我们模拟的Wen-plaquette自旋晶格模型存在两种不同的拓扑序。由于不同的拓扑序具有相同的对称性,这是不能由经典的朗道对称破缺理论描述的一种新型相变现象。该工作为研究当前有着广泛兴趣的拓扑系统上迈出了新的重要一步。内容详见3.1节。 (ii)实验观测了二、三、四自旋量子系统中的动力学量子霍尔效应。通过非绝热响应直接测量Berry曲率和Chern数,清晰地观测到不同的量子化平台即拓扑相变的发生,是目前在最大系统上的非平庸演示。同时,得到的Chern数揭示了哈密顿量的几何结构。类似于传统的量子霍尔效应,精确的量化平台可以用于量子精密测量。内容详见3.2节。 (iii)首次通过测量非阿贝尔几何相实验识别拓扑序。区分多体相互作用量子体系中出现的拓扑有序态是凝聚态理论最重要的任务之一。然而直到目前为止还没有相关的实验报道,主要归结于实验测量本身的极大困难。我们通过测量拓扑简并基态下的非阿贝尔几何相识别出给定某模型的拓扑序,并得到了其准粒子维度和分数统计等信息。与传统的拓扑纠缠熵相比,非阿贝尔几何相提供了更完备的关于拓扑序的信息。这对实验分类不同的拓扑序具有重要意义。内容详见3.3节。2.从量子态制备和存储的角度对拓扑量子计算进行了系列研究： (i)实验制备拓扑序。我们通过绝热驱动含时的多体哈密顿量成功地制备出四重简并的拓扑序。这不仅为进一步研究拓扑序的性质提供了可能。同时,基于基态的拓扑简并和长程纠缠,也为构建具有鲁棒性的量子存储做好了铺垫。内容详见4.1节。 (ii)理论计算和分析拓扑量子存储。我们以Wen-plaquette模型为例,从热噪声和退相干两个角度理论分析了拓扑量子存储的物理机制。并以一个具体的例子来进一步考虑实验演示的可能性。内容详见4.2节。3.开发新的四量子比特核磁样品和脉冲生成自动化程序,不仅提高了实验控制的精确度,也降低了脉冲设计的复杂性。该样品及相关程序已为实验室大量使用,在实验技术改进和提升上有着重要意义。内容详见附录A和B。
[Abstract]:The quantum computer based on the principle of quantum mechanics has the incomparable computing power of the classical computer. However, noise and decoherence are one of the main obstacles to the realization of quantum computers. Noise originates from the imperfect operation of quantum bits; decoherence originates from the inevitable interaction between quantum systems and the environment. Noise and decoherence can cause partial loss or even complete error of the encoding information. One of the solutions is quantum error correction. But this requires additional auxiliary bits to consume too much resources, and the error correction itself is also noisy. Another strategy is topological quantum computing. Unlike active quantum error correction, topological quantum computation is passive, that is, no attempt or operation is required to make the system without noise, because the system itself has a robust self correcting function. This is related to the overall topological properties of the system. Topological quantum computing is a quantum computing scheme with the highest known fault tolerance at present. The topological quantum computing scheme depends on the existence of the topological phase. The topological phase is a kind of strange material state that can not be described by the classical Landau symmetry breaking theory. This state has some interesting properties, such as the base state degeneracy of the topological manifolds, the quasi particle fraction statistics and topological entanglement entropy. A kind of special topological physical state is called topological order, which can be described as a long range entanglement mode with energy gap and has no perturbation effect. The known example is the fractional quantum Holzer state, which is the first time to observe the topological order in a real system. In addition, there is a topological order in some two-dimensional lattice models. Topological ordering not only provides natural noise free media for fault-tolerant quantum computation, but also plays an important role in condensed matter physics as basic scientific research, such as topological properties, topological transformation and discovery of new materials. It is very challenging to observe topology and realize topological quantum computation in a real system, which is mainly limited by the current experimental methods and control techniques. For example, a two-dimensional lattice model is the topological order often involves many body interactions (such as the toric code model with four body interactions), and construct a quantum bit lattice often need more. It is not an easy task to drive and control such a complex multi qubit system. Because of this, the research of topological quantum computing remains in the theory, without any related experimental reports. Quantum simulation, using a controllable quantum system to simulate complex or difficult physical phenomena, has many successful applications in condensed matter physics, high-energy physics and quantum chemistry. Quantum simulation provides us with a powerful means to explore topological and topological quantum computing. On the other hand, as one of the physical implementation platforms of quantum simulation, nuclear magnetic resonance system has mature control technology and precise measurement method in multi qubit experiment, which is a good test platform. During my PhD in nuclear magnetic resonance system of topological quantum simulation and topological quantum computation based on the direction of the theory and a series of experimental studies, the main innovative results are as follows: 1. the use of nuclear magnetic resonance system of topological phase on the quantum simulation: (I) the experimental realization of the adiabatic transition of different topology the order. In the experiment, there are two different topological orders in our simulated Wen-plaquette spin lattice model. Because the different topological order has the same symmetry, it is a new phase transformation phenomenon which can not be described by the classical Landau symmetry breaking theory. The work has taken a new and important step to study the current topology system with wide interest. The content is detailed in Section 3.1. (II) the kinetic quantum Holzer effect in the two or three and four spin quantum systems was experimentally observed. By measuring the Berry curvature and Chern number directly through the adiabatic response, we can clearly observe the occurrence of the different quantization platform, namely the topological transformation, which is a non mediocre demonstration on the largest system at present. At the same time, the obtained Chern number reveals the geometric structure of Hamiltonian. Similar to the traditional quantum Holzer effect, an accurate quantization platform can be used for quantum precision measurement. The content is detailed in Section 3.2. (III) to identify the topological order by measuring the non Abel geometric phase for the first time. It is one of the most important tasks of the condensed state theory to distinguish the topological ordered states appearing in the quantum system of multibody interaction. However, there have been no related experimental reports until now, mainly due to the great difficulty of the experimental measurement itself. We measure the topological order of a given model by measuring the non Abel geometry recognition under topological degenerate ground state, and get the information of quasi particle dimension and fractional statistics. Compared with the traditional topological entanglement entropy, the non Abel geometry provides a more complete information about the topological order. This is of great significance to the classification of different topological order in the experiment. The content is detailed in Section 3.3. 2. from the perspective of quantum state preparation and storage, a series of studies on topological quantum computation are carried out: (I) experimental preparation of topological order. We have successfully prepared four degenerate topological order by adiabatic drive time - containing multibody Hamiltonian. This not only provides a possibility for further study of the properties of the topological order. At the same time, the topology degenerate and long range entanglement based on the ground state also pave the way for the construction of robust quantum storage. The content is detailed in Section 4.1. (II) theoretical calculation and analysis of topological quantum storage. We take the Wen-plaquette model as an example to analyze the physical mechanism of topological quantum storage from two angles of thermal noise and decoherence. And a specific example is given to further consider the possibility of an experimental demonstration. The content is detailed in Section 4.2. 3. the development of new four qubit NMR samples and pulse generation automation program not only improves the precision of experimental control.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413.1;O482.532

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