基于核磁共振体系的若干量子算法的实验验证以及多比特实验技术研究

发布时间：2018-02-09 21:42

本文关键词： 量子计算量子算法核磁共振多比特实验算法冷却　出处：《中国科学技术大学》2017年博士论文　论文类型：学位论文

【摘要】：近年来量子信息与量子计算科学得到了迅速的发展,量子信息处理器被广泛地用于量子计算、量子模拟、量子度量等方面的研究。不断有新的量子算法、量子方案被提出,迫切地要求人们不断提高实验技术手段,使这些算法和方案能够早日被实验实现。核磁共振平台是一个很好的量子方案测试平台,其提供了丰富而又精密的量子操控手段。最近几年很多量子计算方案在此平台上得到实现,并且在此过程中发展了一系列的实验技术。本人在液态核磁共振平台上,对若干量子算法、量子方案进行了实验验证。为了能提高实验可操控量子比特位数以进行更复杂的量子实验,掌握并发展了一系列多比特控制技术,并实现了 7比特标记赝纯态制备。此外提高样品极化度在量子信息处理过程中起着重要的作用,对如何有效提高样品初始极化度做了些理论研究工作。本论文的主要内容如下:1.第一章是对量子计算的背景介绍。简要描述了量子比特、量子逻辑门等基本概念,回顾了一些量子算法,并介绍了几个目前主流的量子计算物理实验体系。2.第二章主要介绍基于核磁共振量子计算的基本概念、模型以及量子操控技术。3.第三章介绍了利用核磁共振技术对若干量子算法的实验演示。第一个工作是实验验证量子线性方程组算法,实验求解了2×2的线性方程组,三组实验得到的实验解误差都只有7%左右,很好地验证了此算法的正确性和有效性。第二个工作是实验验证高斯和算法,利用此算法,实验实现了对整数9和15的square-free判断以及square-free分解。第三个工作是实验验证了 4比特H型魔态提纯方案。4.第四章讨论了有关多量子比特核磁共振体系的实验操控技术。首先讨论了多比特实验中的技术困难,然后结合制备7比特标记赝纯态实验对一系列多比特核磁实验技术进行了描述。5.第五章提出了一种新的基于热库的算法冷却方案。先简要回顾热库算法冷却以及核Overhauser效应,然后利用关联表象下的Redfield方程推导出Γn弛豫过程的具体作用形式。联合Γn弛豫与免退相干子空间,提出新的热库算法冷却方案,进一步提高了冷却的极化度上界。6.第六章是总结与展望。
[Abstract]:In recent years, quantum information and quantum computing science have been developed rapidly. Quantum information processor has been widely used in quantum computing, quantum simulation, quantum measurement and so on. In order to make these algorithms and schemes come true, nuclear magnetic resonance (NMR) platform is a good testing platform for quantum schemes. In recent years, many quantum computing schemes have been implemented on this platform, and a series of experimental techniques have been developed in the process. In order to increase the number of quantum bits that can be controlled in order to carry out more complex quantum experiments, a series of multi-bit control techniques have been mastered and developed. In addition, increasing the polarization of the sample plays an important role in the process of quantum information processing. The main contents of this thesis are as follows: 1. The background of quantum computation is introduced in chapter 1. The basic concepts of quantum bit, quantum logic gate and so on are briefly described. In this paper, we review some quantum algorithms, and introduce some popular quantum computing physics experimental systems .2.Chapter two mainly introduces the basic concepts of quantum computing based on nuclear magnetic resonance. Model and quantum manipulation technology .3.Chapter 3 introduces the experimental demonstration of some quantum algorithms using nuclear magnetic resonance. The first work is to verify the quantum linear equation system algorithm experimentally, and to solve the 2 脳 2 linear equation system experimentally. The error of the three groups of experiments is only about 7%, which proves the correctness and validity of the algorithm. The second work is to test Gao Si and the algorithm. The square-free judgment and square-free decomposition of integers 9 and 15 have been realized in the experiment. The third work is to verify experimentally the scheme of purification of 4-bit H-type magic state. Chapter 4. 4th discusses the experimental manipulating technique of multi-quantum bit nuclear magnetic resonance system. First of all, the technical difficulties in the multi-bit experiment are discussed. Then, a series of multi-bit nuclear magnetic experiments are described with the preparation of 7-bit labeled pseudomorphic states. In Chapter 5. 5th, a new algorithm cooling scheme based on heat reservoir is proposed. Firstly, the cooling of thermal reservoir algorithm and the nuclear Overhauser effect are briefly reviewed. Then, by using the Redfield equation under the correlation representation, the concrete action form of 螕 n relaxation process is derived. A new cooling scheme of heat reservoir algorithm is proposed by combining 螕 n relaxation with non-decoherence subspace. Chapter 6. 6th, which further improves the upper bound of cooling polarization, is a summary and prospect.
【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】：2017
【分类号】：O413

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