Preparing Greenberger-Horne-Zeilinger and $W$ states on a long-range Ising spin model by global controls

Abstract

Entanglement, a unique quantum resource with no classical counterpart, remains at the heart of quantum information. The Greenberger-Horne-Zeilinger (GHZ) and $W$ states are two inequivalent classes of multipartite entangled states which can not be transformed into each other by means of local operations and classic communication. In this paper, we present the methods to prepare the GHZ and $W$ states via global controls on a long-range Ising spin model. For the GHZ state, general solutions are analytically obtained for an arbitrary-size spin system, while for the $W$ state, we find a standard way to prepare the $W$ state that is analytically illustrated in three- and four-spin systems and numerically demonstrated for larger-size systems. The number of parameters required in the numerical search increases only linearly with the size of the system.

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• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Controllability of Symmetric Spin Networks
• Controlled generation of genuine multipartite entanglement in Floquet Ising spin models
• Dynamical Decomposition of Bilinear Control Systems subject to Symmetries
• Accelerating Quantum Optimal Control of Multi-Qubit Systems with Symmetry-Based Hamiltonian Transformations
• Geometric Quantum Machine Learning with Horizontal Quantum Gates
• Engineering Precise and Robust Effective Hamiltonians
• Subspace controllability of bipartite symmetric spin networks under global control