Modified Newton-Raphson GRAPE methods for optimal control of spin systems

• DOI: 10.1063/1.4949534
• Publication Date: 2016-05-25T19:58:33Z
• Authors: D. L. Goodwin; Ilya Kuprov
• Keywords: Hessian matrix; Quasi-Newton method; Matrix Exponential

Quadratic convergence throughout the active space is achieved for gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that Hessian GRAPE fidelity functional unusually cheap, having same asymptotic complexity scaling as itself. This leads to possibility using very efficient numerical optimization techniques. In particular, Newton-Raphson method with a rational function (RFO) regularized shown work require fewer system trajectory evaluations than any other algorithm family. describes algebraic and implementation aspects (matrix exponential recycling, regularization, etc.) RFO version reports benchmarks common spin state problems magnetic resonance spectroscopy.