Coherent Feedback Approach to Continuous Quantum Error Correction

该项目将进行一项理论研究计划，以进一步开发自主量子纠错的新方法。 它将建立在最近分析利用相干反馈的电路设计的结果的基础上，以实现基于简单量子代码的量子存储器，而无需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强大量子信息处理提供新的策略。 以前的工作将扩展到设计基于更复杂的量子码实现量子存储器的相干反馈电路，这些量子码可以纠正任意单量子比特错误，并探索电路压缩等先进概念，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的抽象理论之间的联系，电路理论，因为它存在于电子工程，量子光学/纳米光子学。这个研究项目将提供跨学科的培训，至少有一个研究生，谁将被要求学习相干反馈量子控制理论和理解量子纠错理论的基本方面超出了通常的基本概念。 该研究基本上使用了数学控制理论家最近开发的技术方法，并将其应用于量子信息理论中的重要问题，在此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实例提供了极好的源材料，例如PI现有的研究生课程“应用物理学的估计和控制方法”和“原子和半导体系统的量子器件物理学”。“他们还提供了与工程和应用数学领域的同事的重要联系点，他们可能非常熟悉控制理论及其与电路设计的联系，但从未想过他们的工作与量子物理学的相关性。

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.