Analysis of Effectiveness of Lyapunov Control for Non-generic Quantum States

TL;DR

This paper evaluates a Lyapunov control method for quantum states, demonstrating almost global stability for certain stationary states and exploring its effectiveness beyond ideal conditions, especially for pseudo-pure states.

Contribution

It extends Lyapunov control analysis to non-generic quantum states, providing stability results and effectiveness assessments under broader conditions.

Findings

Almost global asymptotic stability for stationary target states.

Effectiveness of Lyapunov control varies with Hamiltonian conditions.

Additional analysis for pseudo-pure states using alternative tools.

Abstract

A Lyapunov-based control design for natural trajectory-tracking problems is analyzed for quantum states where the analysis in the generic case is not applicable. Using dynamical systems tools we show almost global asymptotic stability for stationary target states subject to certain conditions on the Hamiltonians, and discuss effectiveness of the design when these conditions are not satisfied. For pseudo-pure target states the effectiveness of the design is studied further for both stationary and non-stationary states using alternative tools.