Parametric multi-element coupling architecture for coherent and dissipative control of superconducting qubits

TL;DR

The paper tackles the challenge of scalable control in superconducting-qubit processors by introducing a parametric multi-element coupler that uses Floquet-engineered interactions to mediate both qubit-qubit and qubit-resonator couplings, while enabling dissipative reset, leakage recovery, and parametric readout through a single coupler. By driving the coupler at harmonics of transition frequencies, the effective couplings ${\tilde{g}_{ij}}$ can be selectively activated, allowing a high-fidelity controlled-Z gate (${F_{CZ}=98.3(0.23)%}$ in ${\tau_{CZ}=339\,\text{ns}}$) and rapid reset (${\mathcal{F}_r=99.8(0.02)%}$ in ${150\,\text{ns}}$) and leakage-recovery (${\mathcal{F}_{LR}=98.5(0.3)%}$ in ${310\,\text{ns}}$) on a single device with a shared resonator. The parametric readout demonstrates single-shot fidelity of ${\mathcal{F}_{meas}=88(0.4)%}$, driven by a tunable qubit-state dependent shift ${\chi}$ in the resonator. Overall, the architecture reduces control hardware and footprint, enhances connectivity, and supports multi-qubit operations and error-correction-friendly readout pathways, with clear paths for further improvement in coherence, drive optimization, and higher-level leakage management.

Abstract

As systems for quantum computing keep growing in size and number of qubits, challenges in scaling the control capabilities are becoming increasingly relevant. Efficient schemes to simultaneously mediate coherent interactions between multiple quantum systems and to reduce decoherence errors can minimize the control overhead in next-generation quantum processors. Here, we present a superconducting qubit architecture based on tunable parametric interactions to perform two-qubit gates, reset, leakage recovery and to read out the qubits. In this architecture, parametrically driven multi-element couplers selectively couple qubits to resonators and neighbouring qubits, according to the frequency of the drive. We consider a system with two qubits and one readout resonator interacting via a single coupling circuit and experimentally demonstrate a controlled-Z gate with a fidelity of $98.30\pm 0.23 \%$, a reset operation that unconditionally prepares the qubit ground state with a fidelity of $99.80\pm 0.02 \%$ and a leakage recovery operation with a $98.5\pm 0.3 \%$ success probability. Furthermore, we implement a parametric readout with a single-shot assignment fidelity of $88.0\pm 0.4 \%$. These operations are all realized using a single tunable coupler, demonstrating the experimental feasibility of the proposed architecture and its potential for reducing the system complexity in scalable quantum processors.

Figures (15)

• Figure 1: Parametric coupling architecture. (a-c) Different architectures consisting of qubits Q (blue squares), flux-tunable couplers C (green circles) and resonators R (yellow triangles). The average number of couplers per qubit $n_c$ and resonators per qubit $n_r$ is given for each configuration. (a) Standard grid with static qubit-resonator interactions and coupler-mediated qubit-qubit interactions. (b) Parametric configuration with two-qubit couplers mediating interactions between qubit pairs and qubit resonators. (c) Four-qubit couplers create a high qubit connectivity and serve as mediators for the qubit resonator interaction. The grey box in (b) and (c) highlights the elemental unit of the parametric coupler architecture. (d) Simplified circuit of the elemental unit used for qubit-resonator interactions. Qubits (blue) and resonator (yellow) are capacitively connected to the coupler (green). The resonator is connected to the $Z_0 = 50Ω$ waveguide impedance via an on-chip feedline. A time-dependent bias current $I(t)$ induces a flux $\varphi_\text{ext}(t)$ in the superconducting quantum interference device (SQUID) loop of the tunable coupler. (e) Energy levels of the qubit and resonator manifold with states labeled $\ket{\text{Q}_1\text{Q}_2\text{R}}$. The black arrows represent the transitions used for reset, leakage recovery, parametric readout and the controlled-Z gate. The resonator relaxation at a rate $\kappa_\text{R}$ is indicated by the red arrows.
• Figure 2: (a) Excited state population $P_e$ of the qubit during the flux drive for zero parametric coupling (red squares), for weak coupling (yellow triangles) and for strong coupling (blue circles). The grey dashed line shows the decay envelope $\kappa_\text{R}/2$ for the underdamped system. The length of the reset pulse is marked by the vertical dashed line at 150ns. Simulated dynamics are shown as black dashed lines. (b) Pulse schemes and histogram of the integrated measurement signal for different experiments: measurement only (grey triangles), reset pulse (green diamonds), $\pi$-pulse (red circles), $\pi$-pulse followed by a reset pulse (blue squares). The width and position of the two Gaussian distributions for ground and excited state preparation (dashed lines) are fitted once and kept constant for the four experiments, with the distribution height as the only free fit parameter.
• Figure 3: (a) Pulse sequence for the leakage randomized benchmarking (RB) experiment containing Clifford gates (Cl), induced leakage (leak), and the leakage recovery operation (LR). (b) Population $P_g$ in the ground state $\ket{g}$ as a function of the number of Clifford gates $\text{n}_\text{Cl}$ for different interleaved randomized benchmarking protocols: reference (black circles), 2% leakage operation (red triangles), 2% leakage operation followed by a LR operation (blue diamonds) and a delay with the same length as leakage and LR operation combined (green squares). Dashed lines are leakage-RB fits. (c) Leakage population in the $\ket{f}$-state extracted from similar measurements as described in (b). (d) Measured equilibrium leakage population $A_2$ and (e) average gate error $\varepsilon$ as a function of the injected leakage $L_\text{Cl}$. Dashed lines are predictions from rate equations and the error rate, respectively (see main text for details). The vertical yellow line in (e) shows the break-even point between the error from leakage and from decoherence during the LR operation.
• Figure 4: Measured amplitude of the transmitted signal $|S_{21}|$ of the resonator as a function of parametric drive frequency $\omega_\text{D}$ and detuning $\delta_p = \omega_p-\omega_\text{R}$ of the probe tone from the undriven resonance frequency $\omega_\text{R}$, with the qubit being prepared either (a) in its ground state $\ket{g}$ or (b) in its excited state $\ket{e}$, for an effective coupling of $\tilde{g}_\text{QR}/2\pi =2.12(0.06)\MHz$. (c) Difference between the resonator frequency for the qubit being in $\ket{g}$ and $\ket{e}$ for varying parametric coupling strength $\tilde{g}_\text{QR}/2\pi = \{0.06, 0.15, 0.41, 0.90, 1.50, 2.12, 2.50\}$ and the detuning $\Delta$ of the parametric drive from the resonance frequency in the frame of the drive. The vertical dashed line indicates the chosen optimal detuning for the parametric readout. The dashed lines are fits to the avoided crossings, see main text for details. (d) Single-shot data of the measured parametric readout of ground $\ket{g}$- and excited $\ket{e}$-state in the in-phase-quadrature (IQ) plane at a detuning $\Delta/2\pi = 4.02MHz$ and an effective coupling of $\tilde{g}_\text{QR}/2\pi =2.12(0.06)\MHz$. (e) Projected histogram of parametric measurement. The dashed lines are Gaussian fits to the signal distributions with the qubit prepared in $\ket{g}$ and $\ket{e}$.
• Figure 5: Two-qubit randomized benchmarking without (blue circles) and with (red triangles) an interleaved controlled-Z gate. The ground state population $P_g$ of qubit 2 is measured for 100 Clifford sequence randomizations each of length $\text{n}_\text{Cl}$. The average error of the controlled-Z gate $\varepsilon_\text{CZ}$ is extracted from the error per Clifford of the baseline RB $\varepsilon_\text{b}$ and the error per Clifford of the interleaved RB $\varepsilon_\text{i}$.