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arXiv:2102.05327 · Physical Review A

Large-scale Greenberger-Horne-Zeilinger states through a topologically protected zero-energy mode in a superconducting qutrit-resonator chain

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

Published Mar 1, 2021• 34 citations
arXivHTMLPDF

Abstract

We propose a superconducting qutrit-resonator chain model, and analytically work out forms of its topological edge states. The existence of the zero-energy mode enables one to generate a state transfer between two ends of the chain, accompanied with state flips of all intermediate qutrits, based on which $N$-body Greenberger-Horne-Zeilinger (GHZ) states can be generated with great robustness against disorders of coupling strengths. Three schemes of generating large-scale GHZ states are designed, each of which possesses the robustness against loss of qutrits or of resonators, meeting a certain performance requirement of different experimental devices. With experimentally feasible qutrit-resonator coupling strengths and available coherence times of qutrits and resonators, it has a potential to generate large-scale GHZ states among dozens of qutrits with a high fidelity. Further, we show the experimental consideration of generating GHZ states based on the circuit QED system, and discuss the prospect of realizing fast GHZ states.

DOI
10.1103/physreva.103.032402

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We propose a superconducting qutrit-resonator chain model, and analytically work out forms of its topological edge states. The existence of the zero-energy mode enables one to generate a state transfer between two ends of the chain, accompanied with state flips of all intermediate qutrits, based on which NNN-body Greenberger-Horne-Zeilinger (GHZ) states can be generated with great robustness against disorders of coupling strengths. Three schemes of generating large-scale GHZ states are designed, each of which possesses the robustness against loss of qutrits or of resonators, meeting a certain performance requirement of different experimental devices. With experimentally feasible qutrit-resonator coupling strengths and available coherence times of qutrits and resonators, it has a potential to generate large-scale GHZ states among dozens of qutrits with a high fidelity. Further, we show the experimental consideration of generating GHZ states based on the circuit QED system, and discuss the prospect of realizing fast GHZ states.
Topological pumping of edge states in the finite lattice with nontrivial topological phases provides a powerful means for robust excitation transfer, requiring extremely slow evolution to follow an adiabatic transfer. Here, we propose fast topological pumping via edge channels to generate large-scale Greenberger-Horne-Zeilinger (GHZ) states in a topological superconducting circuit with a sped-up evolution process. The scheme indicates a conceptual way of designing fast topological pumping related to the instantaneous energy spectrum characteristics rather than relying on the shortcuts to adiabaticity. Based on fast topological pumping, large-scale GHZ states show greater robustness against on-site potential defects, the fluctuation of couplings and losses of the system in comparison with the conventional adiabatic topological pumping. With experimentally feasible qutrit-resonator coupling strengths and moderate decay rates of qutrits and resonators, fast topological pumping drastically improves the scalability of GHZ states with a high fidelity. Our work opens up prospects for the realization of large-scale GHZ states based on fast topological pumping in the superconducting quantum circuit system, which provides potential applications of topological matters in quantum information processing.
Abstract The notion of synthetic dimensions in artificial systems has received considerable attention as it provides novel methods for exploring hypothetical topological matter as well as potential device applications. A superconducting qutrit‐resonator chain is mapped into domain‐divided Su‐Schrieffer–Heeger (SSH) models in the synthetic dimension formed by product states of qutrits and Fock states, which renders single‐excitation transfers to mimic particle transports in 1D potential array. Large‐scale Greenberger–Horne–Zeilinger (GHZ) states can be generated in one‐domain SSH model of synthetic dimension via the topological protected edge channel. Uniquely, a two‐domain SSH model is constructed, and the wave function of the three topological protected states is analytically derived. It is shown that the effective coherent‐tunneling adiabatic passage (CTAP) enables fast large‐scale GHZ state can be generated via topological CTAP. Furthermore, four‐ and multi‐domain SSH models are identified to generate large‐scale GHZ states faster in larger sizes. Numerical results show that topologically generated large‐scale GHZ states exhibit excellent robustness against inevitable variation in ideal hopping rates and losses of systems. The work opens up prospects for realizing fast large‐scale GHZ states in multiple SSH models of synthetic dimension and for facilitating further applications of topological matter in quantum information processing.
We present an efficient method to generate a Greenberger-Horne-Zeilinger (GHZ) entangled state of three cat-state qubits via circuit QED. The GHZ state is prepared with three microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the operation, decoherence caused by the energy relaxation and dephasing of the qutrit is greatly suppressed. The GHZ state is created deterministically, because no measurement is involved. Numerical simulations show that the high-fidelity generation of a three-cqubit GHZ state is feasible with the present circuit QED technology. This proposal can be easily extended to create a N-cqubit GHZ state (N≥3), with N microwave or optical cavities coupled to a natural or artificial three-level atom.
Provided that cavities are initially in a Greenberger-Horne-Zeilinger (GHZ) entangled state, we show that GHZ states of NNN-group qubits distributed in NNN cavities can be created via a three-step operation. The GHZ states of the NNN-group qubits are generated by using NNN-group qutrits placed in the NNN cavities. Here, ``qutrit'' refers to a three-level quantum system with the two lowest levels representing a qubit while the third level acting as an intermediate state necessary for the GHZ state creation. This proposal does not depend on the architecture of the cavity-based quantum network and the way for coupling the cavities. The operation time is independent of the number of qubits. The GHZ states are prepared deterministically because no measurement on the states of qutrits or cavities is needed. In addition, the third energy level of the qutrits during the entire operation is virtually excited and thus decoherence from higher energy levels is greatly suppressed. This proposal is quite general and can in principle be applied to create GHZ states of many qubits using different types of physical qutrits (e.g., atoms, quantum dots, NV centers, various superconducting qutrits, etc.) distributed in multiple cavities. As a specific example, we further discuss the experimental feasibility of preparing a GHZ state of four-group transmon qubits (each group consisting of three qubits) distributed in four one-dimensional transmission line resonators arranged in an array.
We discuss how to generate entangled coherent states of four microwave resonators (a.k.a. cavities) coupled by a three-level superconducting device (qutrit). We also show that a Greenberger-Horne-Zeilinger (GHZ) state of four superconducting qubits embedded in four different resonators can be created with this scheme. In principle, the proposed method can be extended to create an entangled coherent state of nnn resonators and to prepare a (GHZ) state of nnn qubits distributed over nnn cavities in a quantum network. In addition, it is noted that four resonators coupled by a coupler qutrit may be used as a basic circuit block to build a two-dimensional quantum network, which is useful for scalable quantum information processing.