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Proposal for generating and detecting multi-qubit GHZ states in circuit QED

Bishop, LS, Lars Tornberg, Price, D, Eran Ginossar, Andreas Nunnenkamp, Houck, AA, Gambetta, JM, Koch, J, Göran Johansson, S. M. Girvin, Schoelkopf, RJ

Published Jan 1, 2009• 35 citations
OpenAlex

Abstract

We propose methods for the preparation and entanglement detection\nof multi-qubit Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum\nelectrodynamics. Using quantum trajectory simulations appropriate for the\nsituation of a weak continuous measurement, we show that the joint dispersive\nreadout of several qubits can be utilized for the probabilistic production of\nhigh-fidelity GHZ states. When employing a nonlinear filter on the recorded\nhomodyne signal, the selected states are found to exhibit values of the\nBell–Mermin operator exceeding 2 under realistic conditions. We discuss the\npotential of the dispersive readout to demonstrate a violation of the Mermin\nbound, and present a measurement scheme avoiding the necessity for full\ndetector tomography.

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Proposal for generating and detecting multi-qubit GHZ states in circuit QED

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We propose methods for the preparation and entanglement detection of multi-qubit Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum electrodynamics. Using quantum trajectory simulations appropriate for the situation of a weak continuous measurement, we show that the joint dispersive readout of several qubits can be utilized for the probabilistic production of high-fidelity GHZ states. When employing a nonlinear filter on the recorded homodyne signal, the selected states are found to exhibit values of the Bell–Mermin operator exceeding 2 under realistic conditions. We discuss the potential of the dispersive readout to demonstrate a violation of the Mermin bound, and present a measurement scheme avoiding the necessity for full detector tomography.

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Generation of hybrid Greenberger-Horne-Zeilinger entangled states of particlelike and wavelike optical qubits in circuit QED

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Hybrid entanglement between particlelike and wavelike optical qubits has drawn increasing attention because such hybrid entanglement is a key resource in establishing hybrid quantum networks and connecting quantum processors with different encoding qubits. For convenience, we define ``particlelike optical qubits'' as PO qubits and ``wavelike optical qubits'' as WO qubits. In this work, we propose a method to create a hybrid Greenberger-Horne-Zeilinger (GHZ) entangled state of $n$ PO qubits and $n$ WO qubits, by using $2n$ microwave cavities coupled to a superconducting flux qutrit. The two logic states of a PO qubit here are represented by the vacuum state and the single-photon state of a cavity (or represented by the rotated states of the vacuum state and the single-photon state), while the two logic states of a WO qubit are indicated by the two coherent states of a cavity. The procedure for preparing the GHZ state consists of only a few basic operations, and the circuit resources are significantly reduced because of using only one flux qutrit as the coupler. The GHZ-state preparation time does not depend on the number of qubits, and the GHZ state is deterministically generated since no measurement is made. In addition, the intermediate higher-energy level of the qutrit during the entire operation is virtually excited and thus decoherence from this level is greatly suppressed. This proposal is quite general and can be extended to create the proposed hybrid GHZ state, by using a $\mathrm{\ensuremath{\Lambda}}$-type natural or artificial atom coupled to $2n$ microwave or optical cavities. As an example, our numerical simulation demonstrates that within current circuit-QED technology, the hybrid GHZ state of two PO qubits and two WO qubits can be prepared with a high fidelity.

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Deterministic preparation of hybrid GHZ entangled states with a superconducting qubit and multiple photonic qubits

Liang Bin, Lei Chen, Zheqi Yang +6 more

Hybrid entangled states are essential quantum resources not only for hybrid quantum communication but also for creating robust hybrid quantum networks and processors.By considering a circuit-cavity quantum electrodynamics (QED) system composed of a superconducting (SC) qutrit (a three-level quantum system) and n microwave cavities, we here present a method to prepare hybrid Greenberger-Horne-Zeilinger (GHZ) entangled states of n+1 qubits.The use of a single SC qutrit as the coupler leads to a significant saving in circuit hardware resources.The GHZ state preparation is deterministic without measurement.The operation time for the GHZ state preparation is independent of the number of qubits.Decoherence from the highest energy level of the SC qutrit is suppressed because this level remains unoccupied during the GHZ state preparation.Our numerical simulations demonstrate that the high-fidelity generation of hybrid GHZ states of an SC qubit and three photonic qubits is achievable within current circuit-QED technology.The proposed scheme possesses universality and is suitable for preparing hybrid GHZ states of a matter qubit (e.g., atomic qubit, trapped ion, quantum dot, magnon, NV center, and SC qubit with various types) and multiple photonic qubits across a wide range of physical systems.

Chinese Optics Letters•Jan 1, 2025•1 citation
We propose methods for the preparation and entanglement detection\nof multi-qubit Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum\nelectrodynamics. Using quantum trajectory simulations appropriate for the\nsituation of a weak continuous measurement, we show that the joint dispersive\nreadout of several qubits can be utilized for the probabilistic production of\nhigh-fidelity GHZ states. When employing a nonlinear filter on the recorded\nhomodyne signal, the selected states are found to exhibit values of the\nBell–Mermin operator exceeding 2 under realistic conditions. We discuss the\npotential of the dispersive readout to demonstrate a violation of the Mermin\nbound, and present a measurement scheme avoiding the necessity for full\ndetector tomography.
We propose methods for the preparation and entanglement detection of multi-qubit Greenberger–Horne–Zeilinger (GHZ) states in circuit quantum electrodynamics. Using quantum trajectory simulations appropriate for the situation of a weak continuous measurement, we show that the joint dispersive readout of several qubits can be utilized for the probabilistic production of high-fidelity GHZ states. When employing a nonlinear filter on the recorded homodyne signal, the selected states are found to exhibit values of the Bell–Mermin operator exceeding 2 under realistic conditions. We discuss the potential of the dispersive readout to demonstrate a violation of the Mermin bound, and present a measurement scheme avoiding the necessity for full detector tomography.
We present an efficient method to generate a Greenberger-Horne-Zeilinger (GHZ) entangled state of three cat-state qubits via circuit QED. The GHZ state is prepared with three microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the operation, decoherence caused by the energy relaxation and dephasing of the qutrit is greatly suppressed. The GHZ state is created deterministically, because no measurement is involved. Numerical simulations show that the high-fidelity generation of a three-cqubit GHZ state is feasible with the present circuit QED technology. This proposal can be easily extended to create a N-cqubit GHZ state (N≥3), with N microwave or optical cavities coupled to a natural or artificial three-level atom.
In a solid-state circuit QED system, we extend the previous study of generating and stabilizing a two-qubit Bell state [Phys. Rev. A 82, 032335 (2010)] to a three-qubit GHZ state. In a dispersive regime, we employ the homodyne joint readout for multiple qubits to infer the state for further processing, and in particular we use it to stabilize the state directly by means of an alternate-flip-interrupted Zeno (AFIZ) scheme. Moreover, the state-of-the-art feedback action based on the filtered current enables not only a deterministic generation of the pre-GHZ state in the initial stage, but also a fast recovery from occasional error in the later stabilization process. We show that the proposed scheme can maintain the state with high fidelity if the efficient quantum measurement and rapid single-qubit rotations are available.
Hybrid entanglement between particlelike and wavelike optical qubits has drawn increasing attention because such hybrid entanglement is a key resource in establishing hybrid quantum networks and connecting quantum processors with different encoding qubits. For convenience, we define ``particlelike optical qubits'' as PO qubits and ``wavelike optical qubits'' as WO qubits. In this work, we propose a method to create a hybrid Greenberger-Horne-Zeilinger (GHZ) entangled state of nnn PO qubits and nnn WO qubits, by using 2n2n2n microwave cavities coupled to a superconducting flux qutrit. The two logic states of a PO qubit here are represented by the vacuum state and the single-photon state of a cavity (or represented by the rotated states of the vacuum state and the single-photon state), while the two logic states of a WO qubit are indicated by the two coherent states of a cavity. The procedure for preparing the GHZ state consists of only a few basic operations, and the circuit resources are significantly reduced because of using only one flux qutrit as the coupler. The GHZ-state preparation time does not depend on the number of qubits, and the GHZ state is deterministically generated since no measurement is made. In addition, the intermediate higher-energy level of the qutrit during the entire operation is virtually excited and thus decoherence from this level is greatly suppressed. This proposal is quite general and can be extended to create the proposed hybrid GHZ state, by using a $\mathrm{\ensuremath{\Lambda}}$-type natural or artificial atom coupled to 2n2n2n microwave or optical cavities. As an example, our numerical simulation demonstrates that within current circuit-QED technology, the hybrid GHZ state of two PO qubits and two WO qubits can be prepared with a high fidelity.
Important tasks in cavity quantum electrodynamics include the generation and control of quantum states of spatially separated particles distributed in different cavities. An interesting question in this context is how to prepare entanglement among particles located in different cavities, which are important for large-scale quantum information processing. We here consider a multi-cavity system where cavities are coupled to a superconducting (SC) qubit and each cavity hosts many SC qubits. We show that all intra-cavity SC qubits plus the coupler SC qubit can be prepared in an entangled Greenberger–Horne–Zeilinger (GHZ) state, by using a single operation and without the need of measurements. The GHZ state is created without exciting the cavity modes; thus greatly suppressing the decoherence caused by the cavity-photon decay and the effect of unwanted inter-cavity crosstalk on the operation. We also introduce two simple methods for entangling the intra-cavity SC qubits in a GHZ state. As an example, our numerical simulations show that it is feasible, with current circuit-QED technology, to prepare high-fidelity GHZ states, for up to nine SC qubits by using SC qubits distributed in two cavities. This proposal can in principle be used to implement a GHZ state for an arbitrary number of SC qubits distributed in multiple cavities. The proposal is quite general and can be applied to a wide range of physical systems, with the intra-cavity qubits being either atoms, NV centers, quantum dots, or various SC qubits.
Hybrid entangled states are essential quantum resources not only for hybrid quantum communication but also for creating robust hybrid quantum networks and processors.By considering a circuit-cavity quantum electrodynamics (QED) system composed of a superconducting (SC) qutrit (a three-level quantum system) and n microwave cavities, we here present a method to prepare hybrid Greenberger-Horne-Zeilinger (GHZ) entangled states of n+1 qubits.The use of a single SC qutrit as the coupler leads to a significant saving in circuit hardware resources.The GHZ state preparation is deterministic without measurement.The operation time for the GHZ state preparation is independent of the number of qubits.Decoherence from the highest energy level of the SC qutrit is suppressed because this level remains unoccupied during the GHZ state preparation.Our numerical simulations demonstrate that the high-fidelity generation of hybrid GHZ states of an SC qubit and three photonic qubits is achievable within current circuit-QED technology.The proposed scheme possesses universality and is suitable for preparing hybrid GHZ states of a matter qubit (e.g., atomic qubit, trapped ion, quantum dot, magnon, NV center, and SC qubit with various types) and multiple photonic qubits across a wide range of physical systems.