Cross cross resonance gate

TL;DR

The paper introduces the cross-cross resonance (CCR) gate, a two-qubit control scheme for dispersively coupled fixed-frequency transmon qubits that drives both qubits simultaneously at the frequency of the other. The CCR gate yields an effective Hamiltonian with ZX and XZ terms, enabling fast iSWAP- and SWAP-like operations with shorter gate times and reduced leakage compared to the conventional cross-resonance (CR) gate. The authors present a detailed calibration and benchmarking workflow, including dual-drive frequency calibration, gate-time optimization via Cartan decomposition, and channel-purification-assisted tomography, validated by interleaved randomized benchmarking on an IBM quantum device. The results show a ~42.8% reduction in average two-qubit gate error and notable gate-time reductions for iSWAP and SWAP, highlighting the CCR gate as a scalable route to faster entangling gates under limited connectivity. Overall, CCR demonstrates a practical approach to speeding up two-qubit operations while preserving coherence advantages of fixed-frequency transmons, with strong implications for scalable quantum processors.

Abstract

Implementation of high-fidelity swapping operations is of vital importance to execute quantum algorithms on a quantum processor with limited connectivity. We present an efficient pulse control technique, cross-cross resonance (CCR) gate, to implement iSWAP and SWAP operations with dispersively-coupled fixed-frequency transmon qubits. The key ingredient of the CCR gate is simultaneously driving both of the coupled qubits at the frequency of another qubit, wherein the fast two-qubit interaction roughly equivalent to the XY entangling gates is realized without strongly driving the qubits. We develop the calibration technique for the CCR gate and evaluate the performance of iSWAP and SWAP gates The CCR gate shows roughly two-fold improvement in the average gate error and more than 10~\% reduction in gate times from the conventional decomposition based on the cross resonance gate.

Figures (6)

• Figure 1: Heatmaps of qubit excited state population measured after CCR gates with various frequency detunings from the predetermined drive frequencies based on the individual CR gate calibration. Experimental result (a) and simulation result (b). The measured population of Q3 and Q4 are overlaid in the same plot to highlight the optimal driving point. The excited state population of Q3 and Q4 correspond to the red and green, respectively. The yellow-colored region indicates the frequencies where both Q3 and Q4 are simultaneously excited. See discussions in the main text. In each panel, the vertical (horizontal) axis represents the detuning from the predetermined CR frequency of Q4 (Q3) corresponding to the frequency of target qubit Q3 (Q4). The labels in the figure (b) indicate the origin of each transition.
• Figure 2: (a) Desired condition for the entangling gate generated by the CCR drive. (b) Approximated Cartan coefficients of the entangling gates while sweeping the CCR drive duration.
• Figure 3: (a) Gate sequence to generate the iSWAP gate with twice CCR gates. (b) Gate sequence to generate the SWAP gate with three times CCR gates. Experimental results of the two-qubit interleaved randomized benchmarking for the iSWAP (c) and SWAP (d) gate with and without the CCR gates.
• Figure 4: Heatmaps of qubit excited state population measured after CCR gates with various frequency detunings from the predetermined drive frequencies based on the individual CR gate calibration. The measured population of Q3 and Q4 are overlaid in the same plot. In each panel, the vertical (horizontal) axis represents the detuning from the predetermined CR frequency of Q4 (Q3) corresponding to the frequency of target qubit Q3 (Q4). The total duration of the $R_{\mathrm{ZX}}(\pi/4)$ gate is set to (a) $145.8$, (b) $168.0$, and (c) $190.2~\mathrm{ns}$.
• Figure 5: Cartan coefficients of the unitary gate generated by the CCR drive with the static ZZ error $\gamma ZZ~(\gamma\in[0,0.4])$, while sweeping the ratio between the bidirectional CR drive amplitudes as $(1-x):(1+x)~(x\in[-1,1])$. Each line color corresponds to a Cartan coefficient, namely there are three lines for $c_1$, $c_2$ and $c_3$.