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

量子通信和计算提供了安全和高速率的信息传输的可能性，某些重要问题的快速计算解决方案，以及作为现代信息技术核心的量子现象的高效物理模拟。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来使这些过程和机器对量子系统中普遍存在的退相干故障具有健壮性。这一探索涉及到物理、数学、信息论和计算机科学知识的结合，因为出现了新的非经典错误。我的研究努力让我们更接近量子信息可靠传输和处理的目标。从理论上看，我正在寻求构建一种广泛的理论来构建一大类量子纠错码，特别是针对克服非经典错误的障碍，将量子编码理论与经典编码理论中已经研究或正在积极研究的课题联系起来，以便应用经典编码理论中使用的一些成熟的方法和工具来帮助理解量子通信和计算。从实用的角度来看，本文的重点是设计性能优良的量子纠错码，使其在不同的情况下适合于在实际的物理信道中进行高速率的量子信息传输，以及高噪声容限和低资源需求的可靠的量子计算。我还将把这些新颖的量子纠错码应用于量子计算的不同模型的研究，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。这些模型不同于电路模型，为在实践中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.