SKRYN: A fast semismooth-Krylov–Newton method for controlling Ising spin systems

Abstract

The modeling and control of Ising spin systems is of fundamental importance in NMR spectroscopy applications. In this paper, two computer packages, ReHaG and SKRYN, are presented. Their purpose is to set-up and solve quantum optimal control problems governed by the Liouville master equation modeling Ising spin-12 systems with pointwise control constraints. In particular, the MATLAB package ReHaG allows to compute a real matrix representation of the master equation. The MATLAB package SKRYN implements a new strategy resulting in a globalized semismooth matrix-free Krylov–Newton scheme. To discretize the real representation of the Liouville master equation, a norm-preserving modified Crank–Nicolson scheme is used. Results of numerical experiments demonstrate that the SKRYN code is able to provide fast and accurate solutions to the Ising spin quantum optimization problem. Program summaryProgram title: SKRYN, ReHaGCatalogue identifier: AEVN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 8452No. of bytes in distributed program, including test data, etc.: 602389Distribution format: tar.gzProgramming language: MATLAB - (OCTAVE).Computer: Any running Matlab.Operating system: Any running Matlab.RAM: bytesClassification: 4.9.External routines: gmres MATLAB routineNature of problem: Set-up and solution of quantum Ising spin- 1/2 optimal control problems, for NMR spectroscopy applications.Solution method: Krylov-matrix-free implementation of the semismooth NewtonRunning time: 60–600 s