Time Optimal Control of Quantum Information Processing Systems

EIA-0218441 Navin Khaneja哈佛大学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相干操作中的退相干效应。该项目的中心主题是开发一种用于量子网络的最优么正控制的数学理论。由耦合的二能级量子系统组成的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么正演化所需的最短时间，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，重点是对耦合自旋半粒子网络的最优控制(在液态和固态核磁共振中充当量子比特，具有固定相互作用哈密顿量的量子计算和选择性激发某些量子比特的能力)。这个项目的目标之一是发展几何方法来计算在耦合量子系统网络中产生么正演化所需的最小时间的基本界限，并找到达到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所捕捉到的变分思想。寻找控制量子网络动力学的最优策略可以归结为在某些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，我们正在计算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.