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Applied Physics Letters

One-step implementation of a hybrid discrete-variable–continuous-variable phase gate with multiple photonic qubits in circuit QED

Anonymous, Wen Zheng, Yu Zhang, Tong Liu, Shaoxiong Li, Yang Yu

Published Jan 12, 2026• 0 citations
Publisher

Abstract

Quantum phase gates are of fundamental interest in quantum physics and play an important role in quantum communication and quantum computing. Here, we propose a scheme to implement a hybrid discrete-variable–continuous-variable (DV–CV) phase gate on multiple photonic qubits by utilizing multiple control microwave cavities and a single target microwave cavity, all coupled to a common superconducting qutrit (a three-level quantum system) in circuit quantum electrodynamics (QED). In our scheme, two logic states of the target qubit are encoded via the vacuum state and the coherent state (CV state) of the microwave cavity, while two logic states of the control qubits are encoded through the vacuum and single-photon states (DV states) of the microwave cavity. This hybrid DV–CV phase gate enables target qubit to acquire a phase that depends on the total number of control qubits in non-vacuum states, when the target qubit is in the coherent state. Our protocol is extensible and operationally efficient, involving just one step and the measurement of only one target qubit. In addition, as a practical application, this hybrid DV–CV phase gate can be employed as a quantum voting machine. Our numerical simulation demonstrates that the high-fidelity construction of a hybrid three-qubit DV–CV phase gate is feasible with current circuit QED technology.

DOI
10.1063/5.0305064

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Quantum phase gates are of fundamental interest in quantum physics and play an important role in quantum communication and quantum computing. Here, we propose a scheme to implement a hybrid discrete-variable–continuous-variable (DV–CV) phase gate on multiple photonic qubits by utilizing multiple control microwave cavities and a single target microwave cavity, all coupled to a common superconducting qutrit (a three-level quantum system) in circuit quantum electrodynamics (QED). In our scheme, two logic states of the target qubit are encoded via the vacuum state and the coherent state (CV state) of the microwave cavity, while two logic states of the control qubits are encoded through the vacuum and single-photon states (DV states) of the microwave cavity. This hybrid DV–CV phase gate enables target qubit to acquire a phase that depends on the total number of control qubits in non-vacuum states, when the target qubit is in the coherent state. Our protocol is extensible and operationally efficient, involving just one step and the measurement of only one target qubit. In addition, as a practical application, this hybrid DV–CV phase gate can be employed as a quantum voting machine. Our numerical simulation demonstrates that the high-fidelity construction of a hybrid three-qubit DV–CV phase gate is feasible with current circuit QED technology.
We propose to implement a hybrid multi-qubit quantum phase gate based on a setup comprising multiple microwave cavities coupled to a common superconducting transmon qutrit in the circuit quantum electrodynamics. The function of this hybrid quantum phase gate is that a phase related to the total number of cavities in non-vacuum state will be introduced when the transmon qubit is in an excited state. Furthermore, we propose an application, quantum voting machine, with this hybrid quantum gate. This scheme is scalable and simple to operate, requiring just a single step and necessitating only the reading of quantum states of one target qubit. While for quantum voting machine, it ensures the verifiability of the voting results through the measurement of the phase information of the target qubit. Additionally, the anonymity of the voters is ensured as the voting outcome is solely tied to the total number of affirmative votes. Numerical simulations indicate the feasibility of this hybrid quantum gate and quantum voting machine within the current quantum technology.
We present a novel method to realize a multi-target-qubit controlled phase gate with one microwave photonic qubit simultaneously controlling n - 1 target microwave photonic qubits. This gate is implemented with n microwave cavities coupled to a superconducting flux qutrit. Each cavity hosts a microwave photonic qubit, whose two logic states are represented by the vacuum state and the single photon state of a single cavity mode, respectively. During the gate operation, the qutrit remains in the ground state and thus decoherence from the qutrit is greatly suppressed. This proposal requires only a single-step operation and thus the gate implementation is quite simple. The gate operation time is independent of the number of the qubits. In addition, this proposal does not need applying classical pulse or any measurement. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one microwave photonic qubit simultaneously controlling two target microwave photonic qubits is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a natural or artificial Λ-type three-level atom.
We propose an efficient scheme to implement a multiplex-controlled phase gate with multiple photonic qubits simultaneously controlling one target photonic qubit based on circuit quantum electrodynamics (QED). For convenience, we denote this multiqubit gate as MCP gate. The gate is realized by using a two-level coupler to couple multiple cavities. The coupler here is a superconducting qubit. This scheme is simple because the gate implementation requires only one step of operation. In addition, this scheme is quite general because the two logic states of each photonic qubit can be encoded with a vacuum state and an arbitrary non-vacuum state ∣ φ 〉 (e.g., a Fock state, a superposition of Fock states, a cat state, or a coherent state, etc.) which is orthogonal or quasi-orthogonal to the vacuum state. The scheme has some additional advantages: because only two levels of the coupler are used, i.e., no auxiliary levels are utilized, decoherence from higher energy levels of the coupler is avoided; the gate operation time does not depend on the number of qubits; and the gate is implemented deterministically because no measurement is applied. As an example, we numerically analyze the circuit-QED based experimental feasibility of implementing a three-qubit MCP gate with photonic qubits each encoded via a vacuum state and a cat state. The scheme can be applied to accomplish the same task in a wide range of physical system, which consists of multiple microwave or optical cavities coupled to a two-level coupler such as a natural or artificial atom.
In recent years, quantum state engineering and quantum information processing using microwave fields and photons have received increasing attention. In addition, multiqubit gates play an important role in quantum information processing. In this work, we propose to encode a photonic qubit via two arbitrary orthogonal eigenstates (with eigenvalues $\ifmmode\pm\else\textpm\fi{}1$, respectively) of the photon-number parity operator. With such encoding, we then present a single-step method to realize a multi-target-qubit controlled-phase gate with one photonic qubit simultaneously controlling $n\ensuremath{-}1$ target photonic qubits, by employing nnn microwave cavities coupled to one superconducting flux qutrit. This proposal can be applied not only to implement nonhybrid multi-target-qubit controlled-phase gates using photonic qubits with various encodings, but also to realize hybrid multi-target-qubit controlled-phase gates using photonic qubits with different encodings. The gate realization requires only a single-step operation. The gate operation time does not increase with the number of target qubits. Because the qutrit remains in the ground state during the entire operation, decoherence from the qutrit is greatly suppressed. As an application, we show how to apply this gate to generate a multicavity Greenberger-Horne-Zeilinger (GHZ) entangled state with general expression. Depending on the specific encodings, we further discuss the preparation of several nonhybrid and hybrid GHZ entangled states of multiple cavities. We numerically investigate the circuit-QED experimental feasibility of creating a three-cavity spin-coherent hybrid GHZ state. This proposal can be extended to accomplish the same tasks in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a three-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.
Abstract We propose a simple quantum voting machine using microwave photon qubit encoding, based on a setup comprising multiple microwave cavities and a coupled superconducting flux qutrit. This approach primarily relies on a multi-control single-target quantum phase gate. The scheme offers operational simplicity, requiring only a single step, while ensuring verifiability through the measurement of a single qubit phase information to obtain the voting results. It provides voter anonymity, as the voting outcome is solely tied to the total number of affirmative votes. Our quantum voting machine also has scalability in terms of the number of voters. Additionally, the physical realization of the quantum voting machine is general and not limited to circuit quantum electrodynamics. Quantum voting machine can be implemented as long as the multi-control single-phase quantum phase gate is realized in other physical systems. Numerical simulations indicate the feasibility of this quantum voting machine within the current quantum technology.