尾旋系统最优控制的修正Newton-Raphson GRAPE方法
Modified Newton-Raphson GRAPE methods for optimal control of spin systems
摘要：
梯度上升脉冲工程（GRAPE）系列量子最优控制算法实现了整个活动空间的二次收敛。我们证明了在这个通信中，海森的葡萄保真度功能是异常便宜，具有相同的渐近复杂性缩放功能本身。这导致使用非常有效的数值优化技术的可能性。特别是，牛顿-拉夫森方法与有理函数优化（RFO）正则化海森在这项工作中所需的系统轨迹评估比任何其他算法的GRAPE家庭。该通信描述了代数和数值实现方面（矩阵指数循环，Hessian正则化等）。的RFO牛顿-拉夫森版本的GRAPE和报告的基准，在磁共振波谱常见的自旋状态控制问题。
英文摘要：
Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy.
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