Speedup of entanglement generation in hybrid quantum systems through linear driving

Qin-Zhou Ye, Zhen-Tao Liang, Wei-Xin Zhang, De-Jian Pan, Zheng-Yuan Xue, and Hui Yan

Phys. Rev. A 106, 012407 – Published 6 July 2022

Abstract

The hybrid quantum system in which interactions between superconducting (SC) qubits and atomic qubits are mediated by an auxiliary cavity mode is a promising architecture for quantum information processing. However, compared to the strong coupling $g_{1}$ between the SC qubits and the cavity, the coupling $g_{2}$ between the atomic qubits and the cavity is often extremely weak, which limits the operation speed and suffers more from dissipations. Here we propose a built-in fault-tolerant geometric operation to speed up the generation of entanglement between SC qubits and atomic qubits only by linearly driving the qubits. The operation speed is proportional to $\sqrt{g_{1} g_{2}}$ instead of the weaker coupling $g_{2}$ . Comparing with traditional double-swap method, the speedup can reach around 10 times and the fidelity keeps high under current experimental parameters. This speedup technique can be used in various boson-mediated quantum platforms even if parametric driving or modulation of the boson mode is impossible, enabling exploration of fast quantum information processing.

Received 12 October 2021
Revised 6 May 2022
Accepted 27 May 2022

DOI:https://doi.org/10.1103/PhysRevA.106.012407

Physics Subject Headings (PhySH)

Quantum information with hybrid systems

Quantum Information, Science & Technology

Authors & Affiliations

Qin-Zhou Ye^1,2, Zhen-Tao Liang ^1,*, Wei-Xin Zhang¹, De-Jian Pan¹, Zheng-Yuan Xue^1,3, and Hui Yan^1,3,†

¹Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
²School of Electrical Engineering, Guangzhou Railway Polytechnic, Guangzhou 510430, China
³Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China

^*ztliangscnu@163.com
^†yanhui@scnu.edu.cn

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Vol. 106, Iss. 1 — July 2022

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Figure 1
(a) Schematic of a hybrid quantum system consisting of two qubits and an intermediated bosonic field of a cavity. The coupling strength $g_{1}$ between the SC qubit and the cavity mode is usually far stronger than the coupling strength $g_{2}$ between the atomic qubit and the cavity mode. To speed up entanglement generation, an external classic driving field is added to the qubits to induce an unconventional geometric quantum gate between the qubits. (b) A hybrid quantum system consists of a SC qubit, a silicon-vacancy center, and an intermediated high- $Q$ -factor phononic cavity. The qubits are strongly driven by external classic driving fields. The SC qubit and phononic cavity are connected by a piezoelectric transducer. (c) A hybrid quantum system consists of a SC qubit, a Rydberg-atom qubit, and an intermediated high- $Q$ -factor SC 3D rectangular cavity. The qubits are strongly driven by external classic driving fields.
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Figure 2
Comparing the Bell-state generation speed and fidelity of the UGQG method with those of the DS method in the phonon-mediated hybrid SC qubit and silicon-vacancy spin qubit system. (a) Evolution of the density matrix elements in Bell-state generation by the DS method. Inset: the average phonon number in the cavity. $g_{2} / (2 π) = 1$ MHz. (b) Evolution of the density matrix elements in Bell-state generation by the UGQG method. Inset: the average phonon number in the cavity. $g_{2} / (2 π) = 1$ MHz. (c) Bell-state generation time of DS (blue dashed line) and UGQC (red solid line) methods vs $g_{2}$ , represented by $T_{D S}$ and $T_{U G Q G}$ respectively. Inset: the max average phonon number $N_{p}^{\max}$ in the cavity vs $g_{2}$ . (d) The numerical speedup ratio $T_{D S} / T_{U G Q G}$ (red solid line) and the approximate analytic expression for the ratio (blue dashed line) vs $g_{2}$ . (e) and (f) Fidelity of Bell-state generation by DS and UGQG methods vs $g_{2}$ and $κ_{m}$ , respectively. The common parameters are $g_{1} / (2 π) = 50$ MHz, $Γ_{S C} / (2 π) = 5$ kHz, $γ_{S C} / (2 π) = 5$ kHz, and $γ_{S} / (2 π) = 10$ kHz.
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Figure 3
Comparing the Bell-state generation fidelity vs $g_{2}$ and $κ_{c}$ of (b) the UGQG method with that of (a) the DS method in the microwave-photon-mediated hybrid SC qubit and Rydberg-atom qubit system. The parameters are $g_{1} / (2 π) = 100$ MHz, $Γ_{S C} / (2 π) = 5$ kHz, $γ_{S C} / (2 π) = 5$ kHz, $Γ_{g} / (2 π) = 0.4$ kHz, $Γ_{e} / (2 π) = 0.8$ kHz, and $γ_{R} / (2 π) = 0.8$ kHz.
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Figure 4
The populations of $| e g 〉$ and $| g e 〉$ vs time $t$ described by the exact equation (2) and the effective Hamiltonian (3) when $g_{1} / (2 π) = 20$ MHz, $g_{2} / (2 π) = 1$ MHz, $Ω_{d} = 50 g_{1}$ , and $κ_{c} / (2 π) = 1$ kHz. Other parameters are the same as those in Fig. 3 in the main text.
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