Time Optimal Control of Quantum Information Processing Systems

量子信息处理系统的时间最优控制量子力学系统的时间最优控制可以显著地减小相干操纵量子现象中的退相干效应。该项目的中心主题是开发量子网络最优酉控制的数学理论。耦合两能级量子系统的网络形成量子计算机的基准。找到在耦合量子系统网络中产生期望的幺正演化所需的最小时间不仅在量子信息处理领域而且在整个相干光谱学领域都具有根本的实际重要性。特别是，重点是耦合自旋半粒子网络的最佳控制（在液体和固体NMR量子计算中充当量子位，具有固定的相互作用哈密顿量和选择性激发某些量子位的能力）。该项目的目标之一是开发几何方法，用于计算耦合量子系统网络中产生幺正演化所需的最小时间的基本界限，并找到实现这些界限的时间最优控制律。这些方法是基于变分的想法，捕捉到的最优控制理论。寻找控制量子网络动力学的最佳策略可以归结为黎曼几何中计算某些齐性空间中的次黎曼测地线的问题。使用这些几何技术，量子网络的时间最优控制策略正在计算中。

EIA-0218441Navin KhanejaHarvard UniversityTime Optimal Control of Quantum Information Processing SystemsTime optimal control of quantum mechanical systems can significantly minimize decoherence effects in coherent manipulation of quantum pheonomenon. The central theme of the project is to develop a mathematical theory for optimal unitary control of quantum networks. Network of coupled two level quantum systems form the benchmark for a quantum computer. Finding the minimum time it takes to produce a desired unitary evolution in a network of coupled quantum systems is of fundamental practical importance not just in the field of quantum information processing but the whole field of coherent spectroscopy. In particular, focus is on optimal control of network of coupled spin half particles (acting as qubits in liquid and solid state NMR quantum conputing with fixed interaction Hamiltonian and ability to selectively excite some of the qubits. One of the goals of this project is to develop geometric methods for computing fundamental bounds on the minimum time it takes to produce unitary evolution in a network of coupled quantum systems and find time optimal control laws which achieve these bounds. These methods are based on variational ideas as captured by the theory of optimal control. Finding optimal strategies to control the dynamics of quantum networks can be reduced to problems in Riemannian geometry of computing subriemannian geodesics in certain homogeneous spaces. Using these geometric techniques time optimal control strategies for quantum networks are being computed.