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

TL;DR

This paper introduces a modified Newton-Raphson GRAPE method with quadratic convergence for quantum control of spin systems, utilizing an efficient Hessian computation to reduce trajectory evaluations.

Contribution

It presents a novel RFO-regularized Newton-Raphson approach for GRAPE that improves efficiency and convergence in quantum optimal control of spin systems.

Findings

Requires fewer trajectory evaluations than other GRAPE algorithms

Achieves quadratic convergence throughout the active space

Demonstrates effectiveness in magnetic resonance spin control problems

Abstract

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.