Time Evolution Operators for Periodic SU(3)

TL;DR

This paper develops a framework linking time optimal quantum control methods with transforms on SU(3), providing exact solutions for periodic curves and discussing implications for quantum physics and control theory.

Contribution

It introduces a novel methodological framework for solving problems involving SU(3) transformations in quantum control, including exact solutions for periodic curves.

Findings

Exact solutions for periodic curves on SU(3) provided

Transformation laws for time-dependent Hamiltonians derived

Framework applicable to non-simple geometric structures

Abstract

We present an outline of a technique to associate certain methods from time optimal quantum control with various transforms on SU(3). Unitary operators are taken from certain time dependent Hamiltonians and transformation laws are derived. A methodological framework for development of solution for these types of problems with a non-simple geometric framework is presented that is generally applicable. We give an expansive overview of the field of SU(3), its meaning, purpose and context within the presented results. Exact solutions for periodic curves on SU(3) are provided, along with the operators and physical framework that surrounds them. A comprehensive review of the literature and established results is given for reference. Discussion is given in full to effective approaches that may be given both to the teaching of the subject, and the development of further results within the science. We conclude the paper with an overview of new avenues of investigation that are opened through the results that are presented.