Quantum CZ gates on a single gradient metasurface

For the requirement of quantum photonic integration in on-chip quantum information, we propose a scheme to realize quantum controlled-Z (CZ) gates through single gradient metasurface. Using its parallel beam-splitting feature, i.e., a series of connected beamsplitters with the same splitting ratio, one metasurface can support a polarization encoding CZ gate or path encoding CZ gate, several independent CZ gates, and cascade CZ gates. Taking advantage that the path of output state is locked by the polarization of input state, path encoding CZ gates can efficiently filter out bit-flip errors coming from beam-splitting processes. These CZ gates also have the potential to detect quantum errors and generate high-dimensional entanglement through multi-degree-of-freedom correlation on metasurfaces. By integrating quantum CZ gates into a single metasurface, our results open an avenue for high-density and multifunctional integration of quantum devices.