Modified Newton-Raphson methods for optimal control of quantum systems
David L. Goodwin, Ilya Kuprov · arXiv (Cornell University) · 2015
Quadratic convergence throughout the active space is achieved for the 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 RFO regularized Hessian appears 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.