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Europhysics Letters (EPL)

Constructing multi-target controlled phase gate in circuit QED and its applications

Jin‐Xuan Han, Jin‐Lei Wu, Yan Wang, Yan Xia, Jie Song, Yongyuan Jiang

Published Oct 10, 2019• 7 citations
Publisher

Abstract

We present a one-step scheme in circuit quantum electrodynamics (QED) to realize multi-target controlled phase gates by using one microwave cavity that is coupled capacitively to a superconducting flux qutrit which plays the control role and simultaneously controls n target qutrits embedded in the microwave cavity. A strong classical field is imposed on the control qutrit so as to yield two dressed states, one of which is coded as a logical state. The controlled phase gates can be employed to achieve the creation of entangled states deterministically without any measurement, including the Bell state, the GHZ state, and the cluster state. Numerical simulations demonstrate that the high-fidelity creation of the entangled state is feasible with the constructed controlled phase gate under the present circuit QED technology.

DOI
10.1209/0295-5075/127/50002

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We present a one-step scheme in circuit quantum electrodynamics (QED) to realize multi-target controlled phase gates by using one microwave cavity that is coupled capacitively to a superconducting flux qutrit which plays the control role and simultaneously controls n target qutrits embedded in the microwave cavity. A strong classical field is imposed on the control qutrit so as to yield two dressed states, one of which is coded as a logical state. The controlled phase gates can be employed to achieve the creation of entangled states deterministically without any measurement, including the Bell state, the GHZ state, and the cluster state. Numerical simulations demonstrate that the high-fidelity creation of the entangled state is feasible with the constructed controlled phase gate under the present circuit QED 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 a single-step implementation of a muti-target-qubit controlled phase gate with one catstate qubit ( cqubit ) simultaneously controlling n –1 target cqubits . The two logic states of a cqubit are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with n microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit’s energy relaxation and dephasing is greatly suppressed. The gate implementation is quite simple because only a single-step operation is needed and neither classical pulse nor measurement is required. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one cqubit simultaneously controlling two target cqubits is feasible with present circuit QED technology. This proposal can be extended to a wide range of physical systems to realize the proposed gate, such as multiple microwave or optical cavities coupled to a natural or artificial three-level atom.
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.
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.
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.
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.