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Physical Review Applied

Efficient preparation of high-dimensional hybrid entangled states in circuit quantum electrodynamics

Wang-Chu Lv, Wentao Zhao, Yu Wang, Yi‐Hao Kang, Wei Feng, Guoqiang Zhang, Li Zhi Yu, Chui‐Ping Yang, Qi-Ping Su

Published May 14, 2025• 5 citations
Publisher

Abstract

High-dimensional quantum systems, known as qudits with dimension $d>2$, possess the capability to encode and process more information than traditional two-dimensional qubits. Entangled states serve as crucial resources for both quantum computation and quantum communication. On the basis of circuit quantum electrodynamics (QED) systems, we introduce an efficient scheme to deterministically generate high-dimensional multipartite entangled states of hybrid qutrits ($d=3$). Assuming a simple initial state has already been prepared with the use of local operations, our method requires only a single step to produce hybrid Greenberger-Horne-Zeilinger (GHZ) entangled states among circuit QED systems consisting of superconducting qutrits and a superconducting cavity. Remarkably, the number of steps and the operational time remain constant as the number of qutrits increases, highlighting the efficiency and scalability of our approach. Using numerical simulations for a three-dimensional hybrid GHZ state of seven qutrits, we demonstrate the feasibility of our scheme and study the effects of various parameters on the fidelity. The importance of this research is in directing the experimental creation of multipartite, high-dimensional, and hybrid GHZ states, which can then be used to enhance quantum communication protocols and computational processes.

DOI
10.1103/physrevapplied.23.054037

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High-dimensional quantum systems, known as qudits with dimension d>2d>2d>2, possess the capability to encode and process more information than traditional two-dimensional qubits. Entangled states serve as crucial resources for both quantum computation and quantum communication. On the basis of circuit quantum electrodynamics (QED) systems, we introduce an efficient scheme to deterministically generate high-dimensional multipartite entangled states of hybrid qutrits (d=3d=3d=3). Assuming a simple initial state has already been prepared with the use of local operations, our method requires only a single step to produce hybrid Greenberger-Horne-Zeilinger (GHZ) entangled states among circuit QED systems consisting of superconducting qutrits and a superconducting cavity. Remarkably, the number of steps and the operational time remain constant as the number of qutrits increases, highlighting the efficiency and scalability of our approach. Using numerical simulations for a three-dimensional hybrid GHZ state of seven qutrits, we demonstrate the feasibility of our scheme and study the effects of various parameters on the fidelity. The importance of this research is in directing the experimental creation of multipartite, high-dimensional, and hybrid GHZ states, which can then be used to enhance quantum communication protocols and computational processes.
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.
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.
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.
Hybrid W entangled states are essential in quantum information processing, quantum communication, and quantum technology. In this Letter, we propose a simple method to prepare hybrid W entangled states between n superconducting (SC) qubits and n microwave resonators (MRs) in circuit QED. Only two basic operations are needed for the preparation of hybrid W states. The operational time decreases as the number of qubits increases. Since no ancillary cavity is required, the hardware resources for the state preparation are minimized. Because the state preparation does not involve any measurements, the hybrid W entangled states are generated in a deterministic way. Moreover, during the entire preparation, the high-energy levels of the SC qutrits remain unexcited, which greatly reduces decoherence of the SC qutrits. As an example, our numerical simulation demonstrates that high-fidelity preparation of the hybrid W entangled state of three SC qubits and three MRs is feasible within the current circuit QED technique. This method is universal and can be applied to generate hybrid W states of n matter qubits (e.g., atomic qubits, NV center qubits, quantum dot qubits, and magnon qubits) and n photonic qubits in various physical systems.
In recent years, cat-state encoding and high-dimensional entanglement have attracted much attention. However, previous works are limited to generation of entangled states of cat-state qubits (two-dimensional entanglement with cat-state encoding), while how to prepare entangled states of cat-state qutrits or qudits (high-dimensional entanglement with cat-state encoding) has not been investigated. We here propose to generate a maximally-entangled state of multiple cat-state qutrits (three-dimensional entanglement by cat-state encoding) in circuit QED. The entangled state is prepared with multiple microwave cavities coupled to a superconducting flux ququart (a four-level quantum system). This proposal operates essentially by the cavity-qutrit dispersive interaction. The circuit hardware resource is minimized because only a coupler ququart is employed. The higher intermediate level of the ququart is occupied only for a short time, thereby decoherence from this level is greatly suppressed during the state preparation. Remarkably, the state preparation time does not depend on the number of the qutrits, thus it does not increase with the number of the qutrits. As an example, our numerical simulations demonstrate that, with the present circuit QED technology, the high-fidelity preparation is feasible for a maximally-entangled state of two cat-state qutrits. Furthermore, we numerically analyze the effect of the inter-cavity crosstalk on the scalability of this proposal. This proposal is universal and can be extended to accomplish the same task with multiple microwave or optical cavities coupled to a natural or artificial four-level atom.
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