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arXiv:1706.07083 · Physical Review A

Universal controlled-phase gate with cat-state qubits in circuit QED

Yu Zhang, Xiong Zhao, Zhen-Fei Zheng, Li Zhi Yu, Qi-Ping Su, Chui‐Ping Yang

Published Nov 13, 2017• 28 citations
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Abstract

Cat-state qubits (qubits encoded with cat states) have recently drawn intensive attention due to their enhanced lifetimes with quantum error correction. We here propose a method to implement a universal controlled-phase gate of two cat-state qubits via two microwave resonators coupled to a superconducting transmon qutrit. During the gate operation, the qutrit remains in the ground state; thus decoherence from the qutrit is greatly suppressed. This proposal requires only two basic operations and neither classical pulse nor measurement is needed; therefore the gate realization is simple. Numerical simulations show that high-fidelity implementation of this gate is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate with two microwave resonators or two optical cavities coupled to a single three-level natural or artificial atom.

DOI
10.1103/physreva.96.052317

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Cat-state qubits (qubits encoded with cat states) have recently drawn intensive attention due to their enhanced lifetimes with quantum error correction. We here propose a method to implement a universal controlled-phase gate of two cat-state qubits via two microwave resonators coupled to a superconducting transmon qutrit. During the gate operation, the qutrit remains in the ground state; thus decoherence from the qutrit is greatly suppressed. This proposal requires only two basic operations and neither classical pulse nor measurement is needed; therefore the gate realization is simple. Numerical simulations show that high-fidelity implementation of this gate is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate with two microwave resonators or two optical cavities coupled to a single 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.
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 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.
Compared with a qubit, a qudit (i.e., a ddd-level or ddd-state quantum system) provides a larger Hilbert space to store and process information. On the other hand, qudit-based hybrid quantum computing usually requires performing hybrid quantum gates with qudits that are different in their nature or in their encoding format. In this work, we consider the qutrit case, i.e., the case for a qudit with d=3d=3d=3. We propose a simple method to realize a hybrid quantum controlled-sum gate with one superconducting (SC) qutrit and a cat-state qutrit. This gate plus single-qutrit gates form a universal set of ternary logic gates for quantum computing with qutrits. Our proposal is based on circuit QED and operates essentially by employing a SC ququart (a four-level quantum system) dispersively coupled to a microwave cavity. The gate implementation is quite simple because it only requires a single basic operation. Neither classical pulse nor measurement is needed. The auxiliary higher energy level of the SC ququart is virtually excited during the gate operation, thus decoherence from this level is greatly suppressed. As an application of this gate, we discuss the generation of a hybrid maximally entangled state of one SC qutrit and one cat-state qutrit. We further analyze the experimental feasibility of creating such a hybrid entangled state in circuit QED. This proposal is quite general and can be extended to accomplish the same task in a wide range of physical system, such as a four-level natural or artificial atom coupled to an optical or microwave cavity.
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 propose a method for transferring quantum entangled states of two photonic cat-state qubits ( cqubits ) from two microwave cavities to the other two microwave cavities. This proposal is realized by using four microwave cavities coupled to a superconducting flux qutrit. Because of using four cavities with different frequencies, the inter-cavity crosstalk is significantly reduced. Since only one coupler qutrit is used, the circuit resource is minimized. The entanglement transfer is completed with a singlestep operation only, thus this proposal is quite simple. The third energy level of the coupler qutrit is not populated during the state transfer, therefore decoherence from the higher energy level is greatly suppressed. Our numerical simulations show that high-fidelity transfer of two- cqubit entangled states from two transmission line resonators to the other two transmission line resonators is feasible with current circuit QED technology. This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems, such as four microwave or optical cavities, which are coupled to a natural or artificial three-level atom.