Tuning and amplifying the interactions in superconducting quantum circuits with subradiant qubits

Qi-Ming Chen, Fabian Kronowetter, Florian Fesquet, Kedar E. Honasoge, Yuki Nojiri, Michael Renger, Kirill G. Fedorov, Achim Marx, Frank Deppe, and Rudolf Gross

Phys. Rev. A 105, 012405 – Published 3 January 2022

Abstract

We propose a tunable coupler consisting of $N$ fixed-frequency qubits, which can tune and even amplify the effective interaction between two superconducting quantum circuits. The tuning range of the interaction is proportional to $N$ , with a minimum value of zero and a maximum that can exceed the physical coupling rates between the coupler and the circuits. The effective coupling rate is determined by the collective magnetic quantum number of the qubit ensemble, which takes only discrete values and is free from collective decay and decoherence. Using single-photon $π$ -pulses, the coupling rate can be switched between arbitrary choices of the initial and final values within the dynamic range in a single step without going through intermediate values. A cascade of the couplers for amplifying small interactions or weak signals is also discussed. These results should not only stimulate interest in exploring the collective effects in quantum information processing, but also enable development of applications in tuning and amplifying the interactions in a general cavity-QED system.

Received 6 July 2021
Accepted 22 December 2021

DOI:https://doi.org/10.1103/PhysRevA.105.012405

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Quantum computation Quantum information processing Superconducting quantum optics

Superconducting devices

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Qi-Ming Chen ^1,2,*, Fabian Kronowetter^1,2, Florian Fesquet^1,2, Kedar E. Honasoge^1,2, Yuki Nojiri^1,2, Michael Renger ^1,2, Kirill G. Fedorov^1,2, Achim Marx ¹, Frank Deppe^1,2,3,†, and Rudolf Gross ^1,2,3,‡

¹Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
²Physik-Department, Technische Universität München, 85748 Garching, Germany
³Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 Munich, Germany

^*qiming.chen@wmi.badw.de
^†frank.deppe@wmi.badw.de
^‡rudolf.gross@wmi.badw.de

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Vol. 105, Iss. 1 — January 2022

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Images

Figure 1
(a–c) Schematic of the D-coupler (green) between two resonators, $R_{1}$ and $R_{2}$ , one resonator and one qubit, $R_{1}$ and $Q_{2}$ , as well as two qubits, $Q_{1}$ and $Q_{2}$ , which are colored in red and blue, respectively. The coupler is labeled as $Q_{c}$ , which is an ensemble of $N$ qubits. The effective coupling rate between the two circuits is determined by the collective magnetic quantum number, $m$ , of $Q_{c}$ . (d) A change of the magnetic quantum number, $m \to m^{'}$ , can be realized in a single step by applying $(m^{'} - m)$ single photons to $(m^{'} - m)$ Wilkinson power dividers, each of which couples to two qubits in the ensemble with a $π$ phase difference. We note that the qubit number in the ensemble, $N$ , is assumed to be even, while an odd $N$ leads to a finite minimum coupling rate corresponding to the magnetic quantum numbers $\pm 1 / 2$ . (e) A cascade of $D$ layers of D-couplers (green) to mediate the interaction between two qubits colored in red and blue.
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Figure 2
The optimal number of qubits, $N_{opt}$ , for microwave-optical photon conversion (left) and the absolute effective coupling rate, $| g_{eff} |$ , between the microwave and optical modes (right). Here the coupler frequency, $ω_{c}$ , is swept from the microwave to optical frequency. The dashed line indicates the frequency splitting between the spin- $\pm 1$ and the spin-0 states of an NV center in the electron ground state.
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Figure 3
(a–d) When operating a 80-qubit coupler with different magnetic quantum numbers, $m$ , the two qubits under coupled exchange photons with different Rabi frequency. The interaction can be turned off when $m = 0$ , while the maximum coupling rate, $\pm 4.27 MHz$ , is achieved when $m = \pm 40$ . (e–g) Keeping the parameters unchanged while increasing the number of coupler qubits from 160 to 320, the effective coupling rate increases linearly from $- 8.53 MHz$ through $- 12.80 MHz$ to $- 17.07 MHz$ . In the last case, $| g_{eff} |$ is 1.7 times larger than the physical coupling rate between a single qubit and the coupler. (h) Dynamics of the system with a cascade of two couplers, where each layer contains 240 homogeneous qubits. In all panels, the red and blue curves correspond to the population of the two qubits under coupled, and green curves the magnetic quantum number of the qubit ensemble deviating from $m$ . They are the simulation result with the original Hamiltonians, Eqs. (1) and (6), while the dashed curves correspond to the predictions of the effective Hamiltonians.
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Figure 4
The photon number transition between two qubits, which is mediated by a 10-qubit coupler. From top to the bottom, we perturb the parameters of each single coupler qubit, $ω_{n}$ and $g_{m, n}$ , by $\pm 0.15 %$ , $\pm 1 %$ , and $\pm 1.5 %$ of their ideal values, which follows a uniform distribution in the given range. The other simulation parameters are set identical to that in Fig. 3. In all the panels, the red and blue curves correspond to the population of the two effectively coupled qubits, which are initially prepared in the excited and ground states, respectively. The green curves correspond to the magnetic quantum number of the qubit ensemble deviating from $m = - 5$ , where the coupler qubits are initially in the ground state. The dashed curves correspond to the ideal Rabi oscillation. The simulation is repeated for 50 times, and the inset shows the results in a smaller range.
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