Fast CZ Gate via Energy-Level Engineering in Superconducting Qubits with a Tunable Coupler

TL;DR

Decoherence-induced errors limit two-qubit gate fidelity in superconducting qubits, making ultra-fast CZ gates essential. The authors propose an energy-level engineering strategy in a tunable-coupler architecture to realize a resonant condition $E_{11}=E_{20}=E_{02}$, boosting the effective coupling to $2g$ between $|11\rangle$ and the symmetric state $|B\rangle=(|200\rangle+|020\rangle)/\sqrt{2}$ and enabling a nonadiabatic CZ via Rabi-like oscillations. Using a Transmon–IST pair with opposing anharmonicities and a flux-tunable coupler, the scheme achieves a CZ with $t_{gate}=\pi/(2g_{12})$ and a simulated fidelity $>99.99\%$ in 17 ns, with leakage $<10^{-4}$. The approach remains robust to anharmonicity offsets and suppresses spectator-qubit crosstalk, suggesting a scalable path to deeper quantum circuits on superconducting processors.

Abstract

In superconducting quantum circuits, decoherence errors in qubits constitute a critical factor limiting quantum gate performance. To mitigate decoherence-induced gate infidelity, rapid implementation of quantum gates is essential. Here we propose a scheme for rapid controlled-Z (CZ) gate implementation through energy-level engineering, which leverages Rabi oscillations between the |11> state and the superposition state in a tunable-coupler architecture. Numerical simulations achieved a 17 ns nonadiabatic CZ gate with fidelity over 99.99%. We further investigated the performance of the CZ gate in the presence of anharmonicity offsets. The results demonstrate that a high-fidelity CZ gate with an error rate below 10^-4 remains achievable even with finite anharmonicity variations. Furthermore, the detrimental impact of spectator qubits in different quantum states on the fidelity of CZ gate is effectively suppressed by incorporating a tunable coupler. This scheme exhibits potential for extending the circuit execution depth constrained by coherence time limitations.

Figures (5)

• Figure 1: (a) Schematic of the superconducting circuit featuring a Transmon and an IST qubit coupled via a tunable coupler. (b) Corresponding energy-level diagram demonstrating the condition $E_{110}=E_{200}=E_{020}$ (subscripts denote Q1, Q2, coupler) required for a fast CZ gate. The coupling strengths are denoted by $g_{12}/2\pi=10~\mathrm{MHz}$ (qubit-qubit) and $g_{ic}/2\pi=100~\mathrm{MHz}$ (qubit-coupler, $i=1,2$).
• Figure 2: Mechanisms for conventional and accelerated CZ gate implementation. (a, b) Energy-level diagrams and coupling configurations for conventional CZ gates mediated by the $|110\rangle-|020\rangle$ and $|110\rangle-|200\rangle$ interaction, respectively. (c) Engineered energy-level structure satisfying $\omega_{i}+\alpha_{i}=\omega_{j}~(i,j\in\{1,2\})$. (d) Bloch sphere representation of the state evolution under conventional couplings. (e) Bloch sphere representation of the state evolution between $\left|110\right\rangle$ and $\left|B\right\rangle=\left(\left|200\right\rangle+\left|020\right\rangle\right)/\sqrt{2}$. (f) Coherent oscillation between $\left|110\right\rangle$ and $\left|B\right\rangle$under the effective Hamiltonian.
• Figure 3: (a) Frequency pulse scheme for realizing a fast CZ gate by simultaneously tuning the frequencies of the Transmon and the coupler to shift the system from the idle point to the work point. The anharmonicities are set as $-\alpha_1=\alpha_2=2\pi\times250~\mathrm{MHz}$. (b) Simulated leakage and swap errors of the fast CZ gate as functions of the control parameters defined in (a).
• Figure 4: (a) Control waveform for the CZ gate at $\delta/2\pi=10~\mathrm{MHz}$. The corresponding leakage and swap errors are shown in (c). (b) Control waveform for the CZ gate at $\delta/2\pi=20~\mathrm{MHz}$. The errors are shown in (d). An error below $10^{-4}$ is still achieved, albeit with an increased gate duration compared to the ideal case ($\delta=0$) in Fig. \ref{['Figure3']}.
• Figure 5: (a) Four-qubit lattice configuration. Qubits $Q_{1}$ and $Q_{2}$ are used to implement the CZ gate, while $S_{1}$ and $S_{2}$ serve as spectator qubits. The full quantum state of the system is denoted as $|\mathrm{~Q_1,Q_2,S_1,S_2,C_1,C_2,C_3,C_4}\rangle$, where $C_1-C_4$ represent tunable couplers. (b) CZ gate error under different spectator qubit states. When qubits $S_{1}$ and $S_{2}$ are initialized in states $|00\rangle,|01\rangle,|10\rangle,$ and $|11\rangle$, the CZ gate error between $Q_{1}$ and $Q_{2}$ remains below $10^{-4}$ in all cases.