High-fidelity single-layer gradient metasurface for optical quantum controlled-Y gate

Abstract Two-qubit controlled gates such as the controlled-Y (CY) gate are essential building blocks for universal quantum computation. While linear-optical implementations of CNOT and CZ gates have been realized with discrete optics and integrated waveguides, realizing a faithful CY gate on a compact, single-element platform remains challenging because it requires both a controlled bit-flip and precise ±i phase factors. Here we propose and numerically demonstrate an optical quantum CY gate based on a single-layer Pancharatnam-Berry (PB) gradient metasurface operating at 1550 nm. Polarization-encoded photons are processed by a 26-pillar amorphous-silicon supercell that realizes parallel beam splitting, diffraction routing and two-photon interference. After fixed local polarization encoding/analysis transformations and coincidence post-selection, the reconstructed two-photon gate matrix matches the ideal CY unitary with a matrix fidelity of 0.9885. Computational ZZ- and complementary XY-basis truth tables yield fidelities of 0.9902 and 0.9924, respectively, while the four phase-type Bell states generated by the gate exhibit an average fidelity of 0.9902. The average post-selection success probability extracted from full-wave simulations is 0.0976. Wavelength-dependent simulations including material dispersion indicate a simulated bandwidth of approximately 26.5 nm F_CY≥0.95. The results establish a compact, monolithic metasurface platform for phase-sensitive controlled quantum logic and entangled-state manipulation.