Optimal Control Targeting Maximally Entangled States

Abstract

Greenberger-Horne-Zeilinger (GHZ) states are crucial resources for numerous quantum information processing protocols. We introduce a novel target functional encompassing the entire set of n-qubit GHZ states. We demonstrate its utility by optimizing control fields within a spin chain model to generate arbitrary n-qubit GHZ states across a broad range of evolution times T. While the minimum infidelity for generating specific GHZ states shows temporal oscillations, our arbitrary GHZ state target functional enables the identification of control parameters that yield optimal infidelity across these time variations. The versatility of our target functional proves particularly advantageous when control over the system is limited, as it circumvents the necessity of selecting a specific target GHZ state for optimization.