High-fidelity two-logical-qubit gates are essential for realizing fault-tolerant quantum computation with bosonic codes, yet experimentally reported fidelities have rarely exceeded 90\%. Here, we propose a geometric phase engineering approach for implementing controlled-phase gates for binomially encoded logical qubits. This method leverages the structural simplicity of geometric drives to reduce the numerical optimization dimensionality while fully incorporating system nonlinearities, enabling fast and high-fidelity logical operations. As an example, we experimentally demonstrate a process fidelity of 97.4±0.8\% for a controlled-Z gate between two binomial codes, surpassing all previously reported two-logical-qubit gates in bosonic codes. This work demonstrates that geometric phase engineering provides an effective and experimentally feasible route to fast, high-fidelity logical operations in bosonic quantum processors.
@article{arxiv.2511.06354,
title = {High-Fidelity Controlled-Phase Gate for Binomial Codes via Geometric Phase Engineering},
author = {Yifang Xu and Yilong Zhou and Lida Sun and Hongwei Huang and Zi-Jie Chen and Lintao Xiao and Bo Zhang and Chuanlong Ma and Ziyue Hua and Weiting Wang and Guangming Xue and Haifeng Yu and Weizhou Cai and Chang-Ling Zou and Luyan Sun},
journal= {arXiv preprint arXiv:2511.06354},
year = {2025}
}