The Greenberger-Horne-Zeilinger and W states represent two inequivalent classes of multipartite entangled states that cannot be transformed through local operations and classical communication. The challenge of their interconversion has received considerable attention due to these intrinsic constraints. In this study, we propose a protocol to achieve rapid and deterministic conversion between the W and Greenberger-Horne-Zeilinger states in a spin-chain system based on the inverse-engineering technique. The inherent flexibility of this approach allows for the optimization of energy cost during the conversion process. Furthermore, we present a proof-of-principle experimental demonstration of this protocol on a nuclear magnetic resonance platform. This work highlights the great potential of the inverse-engineering method for rapidly and efficiently manipulating quantum entangled states in many-body systems.

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• Adiabatic quantum optimization
• Entanglement production
• Inverse problems
• Quantum information processing
• Quantum protocols
• Quantum state engineering
• Nuclear magnetic resonance
• Quantum spin chains