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arXiv:2501.18881 · Physical Review Letters

Efficient Preparation of Entangled States in Cavity QED with Grover’s Algorithm

Omar Nagib, Mark E. Saffman, Klaus Mølmer

Published Jun 30, 2025• 8 citations
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Abstract

We propose to employ the amplification mechanism of Grover's search algorithm to efficiently prepare entangled states of an ensemble of qubits. The conditional change of sign employed in the algorithm can be implemented by the phase shift of photons scattered on an optical cavity hosting an atomic ensemble. We show that collective Dicke states, Greenberger-Horne-Zeilinger states, and Schrödinger cat superpositions of N atoms may be prepared deterministically by few (∼N^{1/4}) photon scattering events without individual addressing of the atoms.

DOI
10.1103/3fzf-wsr2

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We propose to employ the amplification mechanism of Grover's search algorithm to efficiently prepare entangled states of an ensemble of qubits. The conditional change of sign employed in the algorithm can be implemented by the phase shift of photons scattered on an optical cavity hosting an atomic ensemble. We show that collective Dicke states, Greenberger-Horne-Zeilinger states, and Schrödinger cat superpositions of N atoms may be prepared deterministically by few (∼N^{1/4}) photon scattering events without individual addressing of the atoms.
We show that iteration of a few ( ∼N1/4\sim N^{1/4}∼N1/4) unitary steps of Grover's algorithm suffices to perfectly prepare a Dicke state of NNN atoms in a cavity. We also show that a few subsequent Grover steps can be employed to generate GHZ and Cat states. The Grover iteration is physically realized by global qubit rotations and by the phase shift of single photons reflected on the cavity. Our protocols are deterministic and require no individual addressing of the atoms. A detailed error analysis accounting for spatial mode matching of the photon to the cavity, spontaneous emission, mirror scattering, and the finite bandwidth of the photon mode is used to predict the fidelity of the prepared states as a function of system parameters and atom-cavity cooperativity. The fidelity can be increased by heralding on detection of the reflected photon.
Abstract The quantum spin states of an atomic ensemble are of special interest to both fundamental studies and precision measurement applications. Here, we propose a scheme to prepare collective quantum states of an atomic ensemble placed in an optical cavity via homodyne measurement of a probing light field. The effective interactions of atoms mediated by photons are enhanced by the optical cavity, and the output probe light could also be entangled with the collective spin states. By selectively measuring the quadrature of the output light, we can prepare various quantum states, including superposition states of Dicke states and Dicke squeezed states. It is also demonstrated that the fidelity of the prepared quantum state can be enhanced by repetitive homodyne detection and using longer probe laser pulses. With the experimental parameters, we discuss some imperfections, including background noise, fluctuation of the measurement outcomes, and free-space scattering.We believe that our scheme should be feasible for experimental realization with current technologies, which may be used in the future study of quantum mechanics and quantum metrology.
Based on a cavity-assisted interaction by single-photon pulses, we propose a scheme to implement a two-qubit Grover search in a distributed quantum network, with qubits encoded in pairs of atoms in a dephasing-free subspace (DFS), which could strongly suppress collective dephasing errors and would be helpful for enhancing the fidelity of implementation. Moreover, we show that the preparation of entangled states and transfer of quantum states can be completed in our improved scheme, which is very important for the compatibility and scalability of the quantum network.
We propose a way for generating nnn-qubit Greenberger-Horne-Zeilinger (GHZ) entangled states with a three-level qubit system and $(n\ensuremath{-}1)$ four-level qubit systems in a cavity. This proposal does not require identical qubit-cavity coupling constants and thus is tolerant to qubit-system parameter nonuniformity and nonexact placement of qubits in a cavity. The proposal does not require adjustment of the qubit-system level spacings during the entire operation. Moreover, it is shown that entanglement can be deterministically generated using this method and the operation time is independent of the number of qubits. The present proposal is quite general, which can be applied to physical systems such as various types of superconducting devices coupled to a resonator or atoms trapped in a cavity.
We propose schemes for generating multiple-atom entangled states and a multiple-photon Greenberger-Horne-Zeilinger state, respectively, based on the input-output relation of the cavity. The numerical simulations show that produced multiple-particle entangled states have high fidelity even if the atoms are not localized in the Lamb-Dicke regime. Some practical quantum noises, such as atomic spontaneous emission and output coupling inefficiency, only decrease the success probability but exert no influence on the fidelity of prepared multiple-particle entangled states. The successful probabilities of our protocols approach unity in the ideal case. In addition, no need for individually addressing keeps the schemes easy to implement from the experimental point of view.