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The convergence of metamaterials and quantum optics heralds a transformative era in photonic technologies, poised to revolutionize applications ranging from information processing and imaging to sensing and beyond. This review explores the synergistic integration of metasurfaces—engineered sub-wavelength planar structures—and quantum optics, which exploits quantum mechanical principles to manipulate light at the most granular level. We outline the design principles, fabrication processes, and computational challenges involved in creating quantum metasurfaces, discussing both forward and inverse design approaches. Advances in nanofabrication and intelligent optimization techniques, such as machine learning and topology optimization, have enabled the development of metasurfaces with unparalleled control over electromagnetic waves. We examine recent progress in using quantum metasurfaces for single-photon and multi-photon generation, quantum imaging, and quantum sensing, showcasing how these innovations achieve unprecedented precision and novel functionalities. Additionally, we highlight the integration of metasurfaces into quantum light manipulation, emphasizing their role in enhancing wavefront shaping and entanglement control. By providing a comprehensive survey of current advancements and future research directions, this review highlights the vast potential of metasurfaces and quantum optics at the crossroads, setting the stage for next-generation technological innovations that will define the forthcoming decade. 

A metastructure-based on a graded-index lens is presented for the terahertz regime as an emulator for quantum algorithms. Further optimization is presented by applying machine learning in an inverse design strategy. 

An all-dielectric photonic metastructure is investigated for application as a quantum algorithm emulator (QAE) in the terahertz frequency regime; specifically, we show implementation of the Deustsh-Josza algorithm. The design for the QAE consists of a gradient-index (GRIN) lens as the Fourier transform subblock and patterned silicon as the oracle subblock. First, we detail optimization of the GRIN lens through numerical analysis. Then, we employed inverse design through a machine learning approach to further optimize the structural geometry. Through this optimization, we enhance the interaction of the incident light with the metamaterial via spectral improvements of the outgoing wave. 

We demonstrate machine-learning-enhanced Bayesian quantum state tomography on near-term intermediate-scale quantum hardware. Our approach to selecting prior distributions leverages pre-trained neural networks incorporating measurement data and en-ables improved inference times over standard prior distributions. 

The development of active metadevices continues to present keystone challenges in fields of plasmonics and photonics. Here, we demonstrate an analogue of electromagnetically induced transparency (EIT) effect in a far-infrared metasurface device via near-field coupling of bright and quasi-dark resonances resonating at nearly the same frequency with contrasting line widths. The proposed metasurface was further optimized numerically in order to demonstrate a reconfiguration effect (frequency-shift of the spectral response). The tunability property of the device is achieved by incorporating a thin layer of Ge 2 Sb 2 Te 5 (GST), a temperature-driven phase change material (PCM). Theoretical analysis based on a coupled Lorentz oscillator model explains the physical mechanism in the proposed design and shows a good agreement with the observed results. Such active hybrid EIT metadevices could have applications in tunable slow-light effects, delay bandwidth management and ultrafast laser induced switching.