Quantum information processing: coding, fault-tolerance, and models

量子通信与计算为安全、高速的信息传输、对某些重要问题的快速计算解决以及对量子现象的高效物理模拟提供了可能，是现代信息技术的核心。然而，量子信息的忠实传输和量子计算机的成功实现依赖于识别合适的纠错码，以使这些过程和机器对量子系统中普遍存在的退相干引起的故障具有鲁棒性。这一探索涉及到物理学、数学、信息论和计算机科学知识的结合，因为会出现新的非经典错误。我的研究努力使我们更接近可靠传输和处理量子信息的目标。从理论的角度,我试图建立一个广泛的理论构建大型量子纠错编码的类,特别是针对克服障碍的非经典的错误链接量子编码理论研究主题,或正积极研究经典编码理论,因此,一些成熟的方法和工具用于帮助的经典编码理论可以应用量子通信和计算的理解。从实用的角度来看，我的重点是设计具有良好性能的量子纠错码，使其在不同情况下适用于通过实际物理通道的高速率量子信息传输，以及具有高噪声容忍度和低资源需求的可靠量子计算。我还将把这些新颖的量子纠错码应用到不同的量子计算模型的研究中，特别是单向量子计算模型、基于隐形传态的量子计算模型和拓扑量子计算模型。除了电路模型之外，这些模型为实际构建大规模量子计算机提供了替代方法。

Quantum communication and computation offer the possibility of secure and high rate information transmission, fast computational solution of certain important problems, and efficient physical simulation of quantum phenomena at the heart of modern information technology. However, faithful transmission of quantum information and successful realization of quantum computers rely upon the identification of suitable error-correcting codes to make such processes and machines robust against faults due to decoherence, ubiquitous in quantum systems. This quest involves a combination of knowledge from physics, mathematics, information theory, and computer science, because new kinds of non-classical errors arise. My research strives to bring us closer to the goal of reliable transmission and processing of quantum information. From the theoretical point of view, I am seeking to construct a broad theory for building a large class of quantum error-correcting codes, particularly aiming at overcoming the barrier of non-classical errors to link quantum coding theory to topics that have been studied or are now actively being studied in classical coding theory, so that some mature methods and tools used in the classical coding theory can be applied for helping with the understanding of quantum communication and computation. From the practical point of view, my focus is on the design of quantum error-correcting codes with nice properties which in different cases make them suitable for high rate quantum information transmission through practical physical channels, and reliable quantum computation with high noise tolerance and low resource requirement. I will also apply these novel quantum error-correcting codes to the study of different models of quantum computation, particularly the one-way quantum computation model, the teleportation-based quantum computation model and the topological quantum computation model. These models other than the circuit model provide alternative approaches for building large-scale quantum computers in practice.