Coherent Feedback Approach to Continuous Quantum Error Correction

该项目将进行一项理论研究计划，以进一步开发一种新的自主量子纠错方法。它将建立在最近的结果基础上，这些结果分析了利用相干反馈的电路设计，以实现基于简单量子代码的量子存储器，而不需要任何外部定时或控制逻辑。这种方法有可能为优化利用物理资源的健壮的量子信息处理贡献新的战略。之前的工作将被扩展到设计相干反馈电路，该电路基于更复杂的量子代码来实现量子存储器，可以纠正任意的单个量子比特错误，并探索电路压缩等高级概念，以利用相干反馈信号的量子力学性质。这项工作将大大加强量子纠错抽象理论、电子工程中的电路理论和量子光学/纳米光子学之间的联系。这项研究项目将为至少一名研究生提供跨学科培训，他们将被要求学习相干反馈量子控制理论，并了解量子纠错理论的基本方面，而不是通常的基本概念。这项研究基本使用了数学控制理论家最近开发的技术方法，并将它们应用于量子信息理论中的重要问题，在这个过程中在这些学科领域之间建立了重要的新桥梁。这些项目为课堂教学中的具体例子提供了极好的素材，如国际和平研究所现有的“应用物理的估计和控制方法”和“原子和半导体系统的量子器件物理”等研究生课程。他们还提供了与工程和应用数学同行的重要联系点，这些同事可能非常熟悉控制理论及其与电路设计的联系，但从未考虑过他们的工作与量子物理的相关性。

This project will pursue a program of theoretical research to further develop a novel approach to autonomous quantum error correction. It will build on recent results which analyzed circuit designs that exploit coherent feedback, to implement quantum memories based on simple quantum codes without any need for external timing or control logic. This approach has the potential to contribute new strategies for robust quantum information processing that make optimal use of physical resources. Previous work will be extended to design coherent feedback circuits that implement quantum memories based on more sophisticated quantum codes that can correct for arbitrary single-qubit errors, and to explore advanced concepts such as circuit compression to exploit the quantum-mechanical nature of coherent feedback signals. The work will substantially strengthen connections among the abstract theory of quantum error correction, circuit theory as it exists in electrical engineering, and quantum optics/nanophotonics.This research project will provide interdisciplinary training for at least one graduate student, who will be required both to learn coherent-feedback quantum control theory and to understand fundamental aspects of quantum error correction theory beyond the usual basic concepts. The research makes essential use of technical methods developed quite recently by mathematical control theorists and applies them to important questions in quantum information theory, building important new bridges between these subject areas in the process. Such projects provide excellent source material for concrete examples in classroom teaching, such as the PI's existing graduate courses in "Estimation and Control Methods for Applied Physics" and "Quantum Device Physics of Atomic and Semiconductor Systems." They also provide important points of contact with colleagues in engineering and applied mathematics, who may be quite familiar with control theory and its connections to circuit design but have never thought of the relevance of their work for quantum physics.