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Quadratic convergence throughout the active space is achieved for thegradient ascent pulse engineering (GRAPE) family of quantum optimal controlalgorithms. We demonstrate in this communication that the Hessian of the GRAPEfidelity functional is unusually cheap, having the same asymptotic complexityscaling as the functional itself. This leads to the possibility of using veryefficient numerical optimization techniques. In particular, the Newton-Raphsonmethod with a rational function optimization (RFO) regularized Hessian is shownin this work to require fewer system trajectory evaluations than any otheralgorithm in the GRAPE family. This communication describes algebraic andnumerical implementation aspects (matrix exponential recycling, Hessianregularization, etc.) for the RFO Newton-Raphson version of GRAPE and reportsbenchmarks for common spin state control problems in magnetic resonancespectroscopy.

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