Long-Range ZZ Interaction via Resonator-Induced Phase in Superconducting Qubits.

Superconducting quantum computing emerges as one of the leading candidates for achieving quantum advantage. However, a prevailing challenge is the coding overhead due to limited quantum connectivity, constrained by nearest-neighbor coupling among superconducting qubits. Here, we propose a novel multimode coupling scheme using three resonators driven by two microwaves, based on the resonator-induced phase gate, to extend the ZZ interaction distance between qubits. We demonstrate a controlled-Z (cz) gate fidelity exceeding 99.9% within 160 ns at a free spectral range (FSR) of 1.4 GHz, and by optimizing driving pulses, we further reduce the residual photon to nearly 10^{-3} within 100 ns at a FSR of 0.2 GHz. These facilitate the long-range cz gate over separations reaching submeters, thus significantly enhancing qubit connectivity and making a practical step toward the scalable integration and modularization of quantum processors. Specifically, our approach supports the implementation of quantum error correction codes requiring high connectivity, such as low-density parity check codes that pave the way to achieving fault-tolerant quantum computing.