As an important degree of freedom (d.o.f.) in photonic integrated circuits, the orthogonal transverse mode provides a promising and flexible way to increase communication capability, for both classical and quantum information processing. To construct large-scale on-chip multimode multi-d.o.f.s quantum systems, a transverse mode-encoded controlled-NOT (CNOT) gate is necessary. Here, with the help of our new transverse mode-dependent directional coupler and attenuator, we demonstrate the first multimode implementation of a 2-qubit quantum gate. The ability of the gate is demonstrated by entangling two separated transverse mode qubits with an average fidelity of $0.89\pm 0.02$ and the achievement of 10 standard deviations of violations in the quantum nonlocality verification. In addition, a fidelity of $0.82\pm 0.01$ is obtained from quantum process tomography used to completely characterize the CNOT gate. Our work paves the way for universal transverse mode-encoded quantum operations and large-scale multimode multi-d.o.f.s quantum systems.

• Received 19 April 2021
• Accepted 25 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.060501