CAREER: Optimal Control of Quantum Systems

[01:36 . 73]在过去的五十年里，人类操纵和控制量子力学现象的能力稳步提高。今天，我们周围的技术直接或间接地归功于量子力学效应。从晶体管、激光、激光唱机、光纤通信、磁共振成像到扫描隧道显微镜，量子技术已经影响了我们生活的方方面面。如今，量子技术专家可以捕获单个原子并进行实验，在精心雕刻的电磁场中上下弹跳原子，并对一个原子一个原子的晶体结构进行成像。近十年来，量子信息科学的兴起为量子力学现象控制的应用增加了一个新的维度。现在，人们越来越重视利用量子动力学来进行计算、通信和信息存储。所有这些技术都涉及对量子力学现象的控制。量子动力学控制的一个核心挑战是系统动力学中的相干性（退相干）的损失，这是由于与环境的不必要的耦合。退相干问题通常出现在几乎所有量子信息设备的潜在实现和量子系统的控制中。在这个项目中，PI将开发受几何控制理论启发的方法，用于量子系统的最优控制。他将计算在量子系统中产生期望进化所需的最小时间的基本界限，并设计实现这些界限的时间最优控制律。这些几何控制思想将应用于高分辨率液态核磁共振（NMR）光谱相干转移实验的时间最优脉冲序列设计，并应用于结构生物学和核磁共振量子计算。时间的最小化是重要的，因为它减少了退相干的影响，提高了核磁共振光谱实验的灵敏度。在不断发展的结构生物学领域，这类工作非常需要，因为时间优化脉冲序列将显著减少光谱仪的时间（在一些实验中以天为单位），从而实现高通量蛋白质结构的测定。时间最优脉冲也将有助于规模核磁共振方法处理更大的蛋白质通过最小化退相干效应。这项工作的范围很广，适用于涉及量子系统控制的各种应用。

0133673KhanejaOver the past fifty years, there has been a steady increase in man's ability to manipulate and control quantum mechanical phenomena. Today we are surrounded with technology that owes its existence directly or indirectly to quantum mechanical effects. From transistors, lasers, compact disc players, optical fibre communications, magnetic resonance imaging to scanning tunneling microscopes, the quantum technology has effected every aspect of our life. These days the quantum technologists can trap and experiment with individual atoms, bounce atoms up and down on carefully sculpted electromagnetic fields, and image the structure of a crystal, atom by atom. Emergence of the science of quantum information in the last decade has added a new dimension to the applications of control of quantum mechanical phenomena. There is now an increasing emphasis on harnessing quantum dynamics for the purposes of computing, communication, and information storage. All these technologies involve exercising control over quantum mechanical phenomena. A central challenge in the control of quantum dynamics is the loss of coherence (decoherence) in system dynamics, due to unwanted couplings to the environment. This issue of decoherence arises in almost all potential implementations of quantum information devices and control of quantum systems in general. In this project the PI will develop methods inspired by geometric control theory for optimal control of quantum systems. He will compute fundamental bounds on the minimum time it takes to produce a desired evolution in a quantum system and design time optimal control laws which achieve these bounds. These geometric control ideas will be applied to design of time optimal pulse sequences for coherence transfer experiments in high resolution liquid state nuclear magnetic resonance (NMR) spectroscopy, with applications to structural biology and NMR quantum computing. Minimization of time is important as it reduces the effects of decoherence and increases the sensitivity of experiments in NMR spectroscopy. There is a great need for such work in the growing field of structural biology, because time optimal pulse sequences will significantly reduce the spectrometer time (by days in some experiments) leading the way to high-throughput determination of protein structures. Time optimal pulses will also help to scale NMR methods for processing of larger proteins by minimizing decoherence effects. This effort is broad in its scope and applicable to a wide variety of applications involving control of quantum systems.