基于簇态的量子纠错码构造方法研究

发布时间：2018-04-12 20:37

本文选题：量子纠错码 + 图态　；参考：《西北大学》2017年硕士论文

【摘要】：在量子计算和量子通信领域,噪声在信息处理中往往会引起错误,所以克服和减少量子噪声的影响就成为了一个关键问题,其中一种有效解决噪声问题的方法就是采用量子纠错码,它在量子计算和量子通信方面中有着很多的应用,如量子容错计算、量子密钥分发和量子纠缠纯化等。本文基于一种拓扑码Toric码的构造机理,将其应用到图态码的领域,提出了一种分步拼接式量子图态码构造方法。先利用图态间的相互作用建立起邻域的纠缠关系,构建出码空间的稳定子主体部分,之后经过计算分析对于不满足纠错条件的构造遗漏之处进行补充,通过增加稳定子操作算符来保证其纠错能力,从而得到完整的稳定子码。将分步拼接式量子图态码构造方法运用在图态上,通过构建环链状结构的图态稳定子得到相应的稳定子码,并对其纠错可行性进行了验证。基于簇态与图态相比较,具有更高纠缠度、更安全、更易制备的优点,所以将分步拼接式量子图态码构造方法进一步运用在簇态上,分别在单列结构、拼接结构、平面结构上,构建“日”字型结构簇态稳定子得到相应的稳定子码,并对其纠错可行性进行了验证。本文中所提出的这种新的量子图态码构造方法可减小主流方法中通过暴力搜索法获得量子图态码时存在的较高复杂度,也可摆脱通过模拟物理模型构造量子纠错码时的种种限制。将构造范围扩展至更高维度的空间时,这种新的量子图态码构造方法仍然适用,并且可以与拓扑码构造规律相结合使用。通过这种新的量子图态码构造方法得出的簇态量子纠错码,具有纠缠度高和保密性强的特点,因此在量子纠错码领域有一定的研究意义与应用前景。
[Abstract]:In the field of quantum computing and quantum communication, noise often causes errors in information processing, so overcoming and reducing the influence of quantum noise becomes a key problem.One of the effective methods to solve the noise problem is to use quantum error-correcting codes, which have many applications in quantum computation and quantum communication, such as quantum fault-tolerant computing, quantum key distribution and quantum entanglement purification.Based on the construction mechanism of a topological code Toric code, this paper applies it to the field of graph-state code, and presents a method of constructing quantum graph-state code with piecewise splicing.Firstly, the entanglement relation of the neighborhood is established by the interaction between graph states, and the stable subbody part of the code space is constructed, and then the missing parts of the structure which do not satisfy the error correction condition are supplemented by calculation and analysis.The error correction ability is guaranteed by adding the stable suboperator, and the complete stable subcode is obtained.The construction method of piecewise quantum graph-state codes is applied to graph states. The corresponding stability subcodes are obtained by constructing the graph-state stabilizers of the ring chain structure, and the feasibility of correcting errors is verified.Based on the advantages of higher entanglement, more security and easier preparation of cluster state compared with graph state, the method of constructing quantum graph state code is further applied to cluster state, in single row structure, splicing structure and plane structure, respectively.The corresponding stable subcodes are obtained by constructing the cluster state stabilizers of the "Sun" font structure, and the feasibility of error correction is verified.This new method of constructing quantum graph-state codes proposed in this paper can reduce the high complexity of obtaining quantum graph-state codes by using the force search method in the mainstream methods.We can also get rid of the limitations of constructing quantum error-correcting codes by simulating physical models.When the construction range is extended to a higher dimensional space, this new method of constructing quantum graph-state codes is still applicable and can be used in combination with topological code construction laws.The cluster-state quantum error-correcting codes obtained by this new method of constructing quantum graph-state codes have the characteristics of high entanglement degree and strong confidentiality, so they have some research significance and application prospect in the field of quantum error-correcting codes.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.2;O413

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