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少量子现象的相干操纵中的退相干效应。该项目的中心主题是发展量子网络最优统一控制的数学理论。耦合两能级量子系统网络构成了量子计算机的基准。寻找在耦合量子系统网络中产生期望的统一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重要的实际意义。特别是，重点是耦合自旋半粒子网络的最优控制（作为液体和固体核磁共振量子计算中的量子比特），具有固定的相互作用哈密顿量和选择性激发某些量子比特的能力。该项目的目标之一是开发几何方法来计算在耦合量子系统网络中产生统一进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。这些方法是基于最优控制理论的变分思想。寻找控制量子网络动力学的最优策略可以归结为在一定齐次空间中计算次黎曼测地线的黎曼几何问题。利用这些几何技术，计算了量子网络的时间最优控制策略。

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.