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arXiv:2504.18074 · Physical Review A

Preparing Greenberger-Horne-Zeilinger states on ground levels of neutral atoms

Zhu-yao Jin, Jun Jing

Published Jul 15, 2025• 7 citations
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Abstract

We propose a scalable protocol in the Rydberg atomic system to generate the Greenberger-Horne-Zeilinger (GHZ) states, where the qubits are encoded on the hyperfine ground levels. Our system is featured with off-resonant driving fields rather than strong Rydberg interaction sufficient for blockade. Closely it can follow the desired nonadiabatic passage during the time evolution and avoid the unwanted transition by imposing the passage-dependent and fast-varying global phase, that serves as an error correction to the universal quantum control. In our protocol, an $N$-qubit GHZ state is prepared in $N-1$ steps, which is found to be robust against both environmental noise and systematic deviation. Our protocol therefore provides an avenue toward large-scale entanglement, which is essential for quantum information processing and computation based on neutral atoms.

DOI
10.1103/c47j-cw46

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We investigate the possibilities for a deterministic conversion between two important types of maximally entangled multiqubit states, namely, WWW and Greenberger-Horne-Zeilinger (GHZ) states, in the Rydberg-blockade regime of a neutral-atom system where each atom is subject to four external laser pulses. Such interconversions between WWW states and their GHZ counterparts have quite recently been addressed using the method of shortcuts to adiabaticity, more precisely techniques based on Lewis-Riesenfeld invariants [R.-H. Zheng et al., Phys. Rev. A 101, 012345 (2020)]. Motivated in part by this recent work, we revisit the WWW to GHZ state-conversion problem using a fundamentally different approach, which is based on the dynamical symmetries of the system and a Lie-algebraic parametrization of its permissible evolutions. In contrast to the previously used invariant-based approach, which leads to a state-conversion protocol characterized by strongly time-dependent Rabi frequencies of external lasers, ours can also yield one with time-independent Rabi frequencies. This feature makes our protocol more easily applicable experimentally, with the added advantage that it allows the desired state conversion to be carried out in a significantly shorter time with the same total laser pulse energy used.
We present a proposal for generation of a robust tripartite Greenberger–Horne–Zeilinger state among three individual neutral Rydberg atoms. By modulating the relation between two-photon detuning and Rydberg interaction strength Uij(r), an effective Raman coupling is obtained between the hyperfine ground states |F=2,M=2〉 of three Rb87 atoms and the Rydberg states |rrr〉 via the third-order perturbation theory. This method is also capable of implementing a three-qubit controlled-phase gate with each qubit encoded into the hyperfine ground states |F=1,M=1〉 and |F=2,M=2〉. As an extension, we generalize our scheme to the case of the multipartite GHZ state and quantum gate in virtue of high-order perturbation theory.
We investigate the possibilities for a deterministic conversion between two important types of maximally-entangled multiqubit states -- namely, W and Greenberger-Horne-Zeilinger (GHZ) states -- in the Rydberg-blockade regime of a neutral-atom system where each atom is subject to four external laser pulses. Such interconversions between W states and their GHZ counterparts have quite recently been addressed using the method of shortcuts to adiabaticity, more precisely techniques based on Lewis-Riesenfeld invariants [R.-H. Zheng {\em et al.}, Phys. Rev. A {\bf 101}, 012345 (2020)]. Motivated in part by this recent work, we revisit the W-to-GHZ state-conversion problem using a fundamentally different approach, which is based on the dynamical symmetries of the system and a Lie-algebraic parametrization of its permissible evolutions. In contrast to the previously used invariant-based approach, which leads to a state-conversion protocol characterized by strongly time-dependent Rabi frequencies of external lasers, ours can also yield one with time-independent Rabi frequencies. This feature makes our protocol more easily applicable experimentally, with the added advantage that it allows the desired state conversion to be carried out in a significantly shorter time.
Large-scale Greenberger-Horne-Zeilinger~(GHZ) state is useful for quantum technologies but difficult to be prepared. Here, we propose fast measurement-based preparation of large-scale GHZ states by a four-qubit quantum phase gate with nuclear-spin qubits of alkaline-earth-like atoms, which is named as quantum ferromagnetic gate~(QFG) due to its analogy to the alignment of molecular magnetic moments in a classical magnet. A high-fidelity Rydberg-mediated QFG can be realized in a time of 6π/Ωm6π/Ω_{\text{m}}6π/Ωm​ with ΩmΩ_{\text{m}}Ωm​ the maximal Rydberg Rabi frequency. From a product state of three data atom and one ancilla atom, a gluing circuit with one QFG, two single-qubit gates, and a projective measurement of the ancilla can generate a 3-qubit GHZ state, and repetition of this gluing circuit can lead to 9, 27, 81, 243, ⋯\cdots⋯-qubit GHZ states. Analyses based on currently available techniques show that a 243-qubit GHZ state is realizable, and more qubits can be entangled with higher detection fidelity.
Greenberger-Horne-Zeilinger (GHZ) state is a typical maximally entangled state which is pursued in both fundamental research and emerging quantum technologies. Preparing large-scale GHZ states in lattice spin systems is particularly appealing for quantum advantages, but conventional schemes face great challenges in scalability. Here we propose a universal and scalable scheme to generate large-scale GHZ-like states, which share similar entanglement and metrological properties with standard GHZ states, in lattice spin systems through global Floquet engineering. Our scheme requires only global operations and shows great advantage for large particle number. It is applicable to systems with arbitrary interaction ranges, offering a practical pathway for large-scale implementation of many-body entangled states in various systems.