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Physical Review A

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

Yu Zhang, Tong Liu, Jun‐Long Zhao, Yang Yu, Chui‐Ping Yang

Published Jun 26, 2020• 24 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.101.062334

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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 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 \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-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.
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.
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.
Typically, multipartite entangled coherent states are difficult to be extended and produced without measurement. We here propose a way to deterministically generate a GHZ (Greenberger–Horne–Zeilinger)-type entangled coherent state of cavities, utilizing a system consisting of a single superconducting qutrit (i.e., a three-level quantum system) and multiple microwave cavities. Due to the use of only a coupler qutrit, the architecture of the circuit system is quite simple. More importantly, our proposal does not require measurement on the state of qutrit compared with the previous proposals. Since the qutrit's third energy level is not populated during the operation, decoherence from the higher energy level is greatly minimized. Furthermore, the entire operation time is independent of the number of microwave cavities. As an example, our numerical simulations show that high-fidelity generation of a three-cavity GHZ-type entangled coherent state is feasible with present circuit quantum electrodynamics technology. This proposal is universal and can be applied to other physical systems, such as microwave or optical cavities, which are coupled to a single natural or artificial three-level atom.
The generation of hybrid entangled states between matter qubits and microwave-field qubits is a fascinating area of quantum science and technology. In this work, we propose an efficient method to deterministically prepare hybrid entangled states between multiple superconducting qubits (matter qubits) and microwave-field qubits (flying qubits), by using a system composed of multiple superconducting qutrits and microwave cavities. Here, each superconducting (SC) qubit is encoded with the two lowest levels of a SC qutrit, while each microwave-field (MF) qubit is encoded using discrete-variable (DV) states (e.g., the vacuum and single-photon states) or continuous-variable (CV) states (e.g., coherent states) of a microwave cavity. Due to the nonpopulation of the qutrits' third energy level during the operation, decoherence from this level is significantly reduced. Moreover, the hybrid entangled states can be generated on a large scale. The operation time is independent of the number of SC qubits and MF qubits. Only two steps of the operation are needed for the preparation of the hybrid Greenberger---Horne---Zeilinger (GHZ) states as long as the initial states of the system are ready. As an example, our numerical results demonstrate that high-fidelity creation of hybrid DV-DV entangled states or CV-DV entangled states of three SC qubits and three MF qubits is feasible with current circuit QED technology. This method is universal and can be extended to generate hybrid entangled states between other matter qubits (such as atoms, ions, quantum dots, NV centers, and magnons) and microwave- or optical-field qubits.
We propose a simple method to realize a hybrid controlled–controlled-Z (CCZ) gate with two photonic qubits simultaneously controlling a superconducting (SC) target qubit, by employing two microwave cavities coupled to a SC ququart (a four-level quantum system). In this proposal, each control qubit is a photonic qubit, which is encoded by two arbitrary orthogonal eigenstates (with eigenvalues ±1, respectively) of the photon-number parity operator. Since the two arbitrary encoding states can take various quantum states, this proposal can be applied to realize the hybrid CCZ gate, for which the two control photonic qubits can have various encodings. The gate realization is quite simple because only a basic operation is needed. During the gate operation, the higher energy intermediate levels of the ququart are not occupied, and, thus, decoherence from these levels is greatly suppressed. We further discuss how to apply this gate to generate a hybrid Greenberger–Horne–Zeilinger (GHZ) entangled state of a SC qubit and two photonic qubits, which takes a general form. As an example, our numerical simulation demonstrates that high-fidelity generation of a cat–cat–spin hybrid GHZ state is feasible within current circuit QED technology. This proposal is quite general, which can be applied to realize the hybrid CCZ gate as well as to prepare various hybrid GHZ states of a matter qubit and two photonic qubits in other physical systems, such as two microwave or optical cavities coupled to a four-level natural or artificial atom.
Hybrid qubits have recently drawn intense attention in quantum computing. We here propose a method to implement a universal controlled-phase gate of two hybrid qubits via two three-dimensional (3D) microwave cavities coupled to a superconducting flux qutrit. For the gate considered here, the control qubit is a microwave photonic qubit (particle-like qubit), whose two logic states are encoded by the vacuum state and the single-photon state of a cavity, while the target qubit is a cat-state qubit (wave-like qubit), whose two logic states are encoded by the two orthogonal cat states of the other cavity. During the gate operation, the qutrit remains in the ground state; therefore, decoherence from the qutrit is greatly suppressed. The gate realization is quite simple, because only a single basic operation is employed and neither classical pulse nor measurement is used. Our numerical simulations demonstrate that with current circuit quantum electrodynamics technology, this gate can be realized with a high fidelity. The generality of this proposal allows implementing the proposed gate in a wide range of physical systems, such as two 1D or 3D microwave or optical cavities coupled to a natural or artificial three-level atom. Finally, this proposal can be applied to create a novel entangled state between a particle-like photonic qubit and a wave-like cat-state qubit.