Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control

• URL: http://arxiv.org/abs/2207.14241v3
• Date: Wed, 30 Nov 2022 16:44:14 GMT
• Title: Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control
• Authors: Vladimir M. Stojanovic, Julian K. Nauth
• Abstract summary: Interconversions of $W$ and Greenberger-Horne-Zeilinger states in various physical systems are attracting considerable attention. We address this problem in the fairly general physical setting of qubit arrays with long-ranged (all-to-all) Ising-type qubit-qubit interaction. Motivated in part by a recent Lie-algebraic result that implies state-to-state controllability, we present a detailed investigation of the state-interconversion problem in the three-qubit case.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Interconversions of $W$ and Greenberger-Horne-Zeilinger states in various physical systems are lately attracting considerable attention. We address this problem in the fairly general physical setting of qubit arrays with long-ranged (all-to-all) Ising-type qubit-qubit interaction, which are simultaneously acted upon by transverse Zeeman-type global control fields. Motivated in part by a recent Lie-algebraic result that implies state-to-state controllability of such a system for an arbitrary pair of states that are invariant with respect to qubit permutations, we present a detailed investigation of the state-interconversion problem in the three-qubit case. The envisioned interconversion protocol has the form of a pulse sequence that consists of two instantaneous (delta-shaped) control pulses, each of them corresponding to a global qubit rotation, and an Ising-interaction pulse of finite duration between them. Its construction relies heavily on the use of the (four-dimensional) permutation-invariant subspace (symmetric sector) of the three-qubit Hilbert space. In order to demonstrate the viability of the proposed state-interconversion scheme, we provide a detailed analysis of the robustness of the underlying pulse sequence to systematic errors, i.e. deviations from the optimal values of its five characteristic parameters.

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