All-Microwave Manipulation of Superconducting Qubits with a Fixed-Frequency Transmon Coupler

Shotaro Shirai, Yuta Okubo, Kohei Matsuura, Alto Osada, Yasunobu Nakamura, and Atsushi Noguchi

Phys. Rev. Lett. 130, 260601 – Published 29 June 2023

Abstract

All-microwave control of fixed-frequency superconducting quantum computing circuits is advantageous for minimizing the noise channels and wiring costs. Here we introduce a swap interaction between two data transmons assisted by the third-order nonlinearity of a coupler transmon under a microwave drive. We model the interaction analytically and numerically and use it to implement an all-microwave controlled-Z gate. The gate based on the coupler-assisted swap transition maintains high drive efficiency and small residual interaction over a wide range of detuning between the data transmons.

Received 20 February 2023
Accepted 1 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.260601

Physics Subject Headings (PhySH)

Quantum control Quantum engineering Quantum information with solid state qubits

Superconducting qubits

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Shotaro Shirai ^1,*, Yuta Okubo ¹, Kohei Matsuura², Alto Osada^1,3, Yasunobu Nakamura ^2,4, and Atsushi Noguchi ^1,4,5,†

¹Komaba Institute for Science (KIS), The University of Tokyo, Meguro-ku, Tokyo 153-8902, Japan
²Department of Applied Physics, Graduate School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
³PRESTO, Japan Science and Technology Agency, Kawaguchi-shi, Saitama 332-0012, Japan
⁴RIKEN Center for Quantum Computing (RQC), Wako, Saitama 351–0198, Japan
⁵Inamori Research Institute for Science (InaRIS), Kyoto-shi, Kyoto 600-8411, Japan

^*shirai-shotaro@g.ecc.u-tokyo.ac.jp
^†u-atsushi@g.ecc.u-tokyo.ac.jp

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Vol. 130, Iss. 26 — 30 June 2023

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Images

Figure 1
(a) Optical images of a fabricated superconducting circuit (top) and three coupled transmons (bottom). Most of the structures are made from TiN electrodes (yellow) on a Si substrate (gray). Inset: scanning electron micrograph of an $Al / {AIO}_{x} / Al$ Josephson junction fabricated with the in situ bandage technique [31]. (b) Equivalent circuit diagram of the coupled transmon system, where readout resonators, Purcell filters, and drive lines are omitted. Only the coupling capacitors connected to them are depicted. $Q_{1}$ , $Q_{2}$ , and $Q_{c}$ represent the two data qubits and one coupler qubit, respectively. (c) Energy-level diagram of the system eigenstates $| i j k ⟩ = | i ⟩_{1} | j ⟩_{2} | k ⟩_{c}$ ( $i, j, k \in {0, 1}$ ) truncated to the first excited state of each transmon. The blue and red arrows are the CAS transitions activated by microwave drives. The dashed energy levels involve the single excitation of the coupler.
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Figure 2
(a) Pulse sequence for the data transmons $Q_{1}$ and $Q_{2}$ , and the coupler transmon $Q_{c}$ to measure the CAS oscillation frequency between the states indicated by the blue arrow in Fig. 1. To activate the transition, we prepare $Q_{2}$ in the first excited state with a $π$ pulse, and then apply a drive pulse to the coupler. (b) Chevron pattern of the blue CAS transition as a function of the detuning $δ = ω_{d} - ω_{b}$ and the pulse duration $τ$ . The white dashed line, $δ = 0$ , shows the resonance condition for the blue CAS transition at $ω_{b} / 2 π ≃ 6.4207 GHz$ . The data are obtained for the coupler drive amplitude $Ω_{d} / 2 π = 72 MHz$ . Note that the blue CAS transition frequency $ω_{b}$ depends on $Ω_{d}$ through the ac Stark shift and the associated correlated oscillations of the excited-state populations of the three transmons are separately observed [32]. (c) Blue and red CAS oscillation frequencies obtained from the fitting. The blue and red solid lines are analytical evaluations, respectively, using Eqs. (6) and (7) with experimentally determined parameters. The dashed lines are the numerical simulations based on Eqs. (1) and (2) using qutip [44, 45]. Inset: $Ω_{d}$ calibration result by driving the fundamental mode of the coupler qubit as a function of the pulse amplitude.
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Figure 3
(a) Pulse sequence for measuring the control phase using the JAZZ protocol [46, 47]. The measurement angle $ϕ$ is swept to find an optimal CAS drive frequency for the cz gate. (b) Controlled phase measured as a function of $δ = ω_{d} - ω_{b}$ , where $ω_{b} / 2 π ≃ 6.4157 GHz$ for the drive amplitude of $Ω_{d} / 2 π = 75 MHz$ . For each drive frequency, we adjust the pulse length so that the coupler returns to the ground state. (c) Ramsey fringes measured with the calibrated detuning of the blue CAS drive. A $π$ phase shift is observed depending on the states of the control transmon $Q_{1}$ . The vertical axis is the signal of $Q_{2}$ normalized to the responses of the ground and excited states of $Q_{2}$ . The black and red dashed curves represent the functions of the ideal cz gate. (d) Interleaved randomized benchmarking (IRB). Blue and red dots are the averaged experimental results of the reference RB and IRB, respectively. The number of randomly generated RB sequences used is 30, and the error bars represent 95% confidence. Dashed lines are fitting curves to the decay model. The horizontal axis is the number of Clifford gates applied. All single-qubit Clifford gates consist of two $X_{π / 2}$ gates and three virtual-Z gates, and the length of the cz gate is 504 ns. Thus, the average duration of the 2-qubit Clifford gate is 945 ns, where each spacing between two successive pulses is set to 6 ns [50].
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Figure 4
Residual $Z Z$ interaction strength $ξ_{Z Z}$ and the drive efficiency $η_{b}$ of the blue CAS transition as a function of the detuning $Δ_{12}$ and transverse coupling strength $g_{i c}$ normalized by the mean anharmonicity $α_{mean} = (α_{1} + α_{2}) / 2$ and detuning $Δ_{i c}, (i \in {1, 2})$ , respectively. Here, $ξ_{Z Z}$ is calculated through numerical diagonalization of Eq. (1) (filled contour plot) using (a) the current and (b) prospective design parameters with the direct transverse coupling $g_{12}$ . The drive efficiency is defined as $η_{b} = Ω_{b} / Ω_{d}$ from Eq. (6) (contour line plot). As the prospective design parameters, we set $(ω_{c} - ω_{1}) / 2 π = 0.6 GHz$ , $ω_{2} / 2 π = 5.0 GHz$ , and $α_{i} / 2 π = (- 0.20, - 0.20, - 0.45) GHz$ for $i = (1, 2, c)$ . The sweep parameters are $ω_{1}$ and $g_{1 c} / Δ_{1 c} = g_{2 c} / Δ_{2 c}$ , and the shaded areas indicate the residual $Z Z$ interaction strength larger than 150 kHz. The green star in (a) indicates the condition in the current experiment.
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