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arXiv:2306.02227 · Physical Review A

One-step implementation of a multi-target-qubit controlled-phase gate with photonic qubits encoded via eigenstates of the photon-number parity operator

Qi-Ping Su, Liang Bin, Yu Zhang, Chui‐Ping Yang

Published Mar 23, 2023• 17 citations
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Abstract

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 $n$ 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.

DOI
10.1103/physreva.107.032616

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Hybrid quantum gates have recently drawn considerable attention. They play significant roles in connecting quantum information processors with qubits of different encoding and have important applications in the transmission of quantum states between a quantum processor and a quantum memory. In this work, we propose a single-step implementation of a multitarget-qubit controlled-not gate with one superconducting (SC) qubit simultaneously controlling nnn target cat-state qubits. In this proposal, the gate is implemented with nnn microwave cavities coupled to a three-level SC qutrit. The two logic states of the control SC qubit are represented by the two lowest levels of the qutrit, while the two logic states of each target cat-state qubit are represented by two quasi-orthogonal cat states of a microwave cavity. This proposal operates essentially through the dispersive coupling of each cavity with the qutrit. The gate realization is quite simple because it requires only a single-step operation. There is no need of applying a classical pulse or performing a measurement. The gate operation time is independent of the number of target qubits, thus it does not increase as the number of target qubits increases. Moreover, because the third higher energy level of the qutrit is not occupied during the gate operation, decoherence from the qutrit is greatly suppressed. As an application of this hybrid multitarget-qubit gate, we further discuss the generation of a hybrid Greenberger-Horne-Zeilinger (GHZ) entangled state of SC qubits and cat-state qubits. As an example, we numerically analyze the experimental feasibility of generating a hybrid GHZ state of one SC qubit and three cat-state qubits within present circuit QED technology. This proposal is quite general and can be extended to implement a hybrid controlled-not gate with one matter qubit (of different type) simultaneously controlling multiple target cat-state qubits in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a three-level natural or artificial atom.
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.
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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.