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    Area of Science:

    • Quantum optics
    • Photonic circuit design
    • Information optics

    Background:

    • Discrete N×N linear unitary operators are crucial in quantum information processing.
    • Previous work established universality using phase shift layers and a fixed discrete fractional Fourier transform (DFrFT).

    Purpose of the Study:

    • To investigate the impact of perturbations and defects on the universality of DFrFT-based photonic circuits.
    • To explore the potential for auto-calibration and error compensation in these optical systems.

    Main Methods:

    • Theoretical analysis of perturbed DFrFT architectures.
    • Investigation of resilience to faulty phase shifters within the layers.

    Main Results:

    • Introducing perturbations to intervening operations does not compromise the universality of the N×N unitary operator architecture.
    • The architecture exhibits resilience to phase shifter defects, tolerating at least one faulty shifter per layer.

    Conclusions:

    • The DFrFT-based photonic circuit architecture is robust against fabrication errors and component defects.
    • These findings enable post-fabrication auto-calibration for universal photonic circuits, enhancing their practical applicability.