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Quantum Science and Technology

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

Dongyan Li, Weihao Zhang, Yaru Li, Guoqiang Lan

Published Aug 25, 2026• 0 citations

Abstract

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 controlled-NOT and controlled-Z 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 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.

DOI: 10.1088/2058-9565/ae9e6c

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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 controlled-NOT and controlled-Z 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 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.

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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.

We propose a scheme to realize quantum controlled-Z (CZ) gates through single gradient metasurface. Using its unique parallel beam-splitting feature, i.e., a series of connected beam splitters with the same splitting ratio, one metasurface can support a CZ gate, several independent CZ gates, or a cascaded CZ gates. Taking advantage of the input polarization determined output path-locking feature, both polarization-encoded and path-encoded CZ gates can be demonstrated on the same metasurface, which further improves the integration level of quantum devices. Our research paves the way for integrating quantum logical function through the metasurface.

Implementing quantum logic gates with linear optical elements is a key approach in photon-based quantum information processing (QIP) due to its operational convenience and experimental flexibility. The adoption of high-dimensional (H-D) quantum computing with qudit encoding over conventional 2-D qubit encoding offers higher information encoding capability. In this paper, we present a linear-optics-based two-qudit 4×4-D (16-D) controlled-SUM (CSUM) gate for photon systems, where the polarization degrees of freedom (DoFs) of two photons encode the 4-D control qudit and the polarization and spatial DoFs of another single photon encode the 4-D target qudit. The 16-D CSUM gate demonstrates an efficiency of 1/243 and a theoretical average fidelity of 0.98395. Additionally, the H-D CSUM gate neither requires ancillary photons and pre-shared entanglement nor presents complex quantum circuits, thus significantly reducing the experimental overhead and enhancing its feasibility with current technology.

Spatial light modulators (SLMs) have emerged as reconfigurable platforms for photonic quantum information processing, offering software-defined control over the orbital angular momentum (OAM) of light encoded in Laguerre-Gaussian (LG) beams. This paper presents a comprehensive simulation and hardware-grounded fidelity analysis of quantum gate operations implemented on the HOLOEYE LC 2012 transmissive SLM. A realistic three-channel noise model comprising 8-bit quantisation noise, twisted-nematic (TN) electronic and thermal noise, and phase-wrap clipping error is obtained from the manufacturer's datasheet without free-parameter fitting, yielding a total noise of

σ_{\text{total}} = 92.4\text{mrad}

. The complete universal single-qubit gate set

\{X, Y, Z, S, T, H\}

and two-qubit entangling gates

\{\text{CNOT}, \text{CZ}, \text{SWAP}\}

are simulated on a

512 \times 512

computational grid. Results show that predicted gate fidelity are in the range of

F = 0.9914\text{--}0.9936

, with fork grating gates limited primarily by TN noise and phase gates achieving higher fidelity owing to zero phase-wrap clipping error. In addition, Bell state preparation via the H-CNOT circuit achieves

F(Φ^+) = 0.9914

after two SLM interactions. We benchmark our obtained results against six published experimental studies spanning the 78%--99.6% fidelity range. Finally, a wavelength-dependent analysis identifies 450--532 nm operation as the optimal regime for this device.