We develop a theoretical and computational framework for estimating and correcting non-Abelian geometric distortions in time-bin photonic qudit processing when the relevant encoded object is a transported logical subspace rather than a collection of independent rays. In such settings, for example under mode mixing, multiplexed routing, or effective degeneracies, the geometric contribution is naturally matrix-valued and is described by a Wilczek-Zee holonomy on a rank-$m$ sub-bundle of the ambient Hilbert space. The framework generalises prior Abelian time-bin Pancharatnam-Berry feed-forward calibration, in which geometric distortions are represented by bin-resolved scalar phases, to the non-Abelian, matrix-valued case. We construct a gauge-covariant discrete estimator from overlap matrices between successive subspace frames: the polar factor of each overlap gives a unitary backward frame comparator, and the adjoint comparators compose to approximate the forward path-ordered exponential of the Wilczek-Zee connection. We prove gauge covariance under frame changes, polar optimality of the local comparator, consistency under partition refinement, and perturbative stability under well-conditioned overlap errors. We then formulate left- and right-acting feed-forward correction rules for removing the estimated holonomy from an effective logical operation. The work does not assume a device-specific transfer matrix, loss model, detector model, or experimental calibration pipeline; numerical studies use synthetic non-Abelian transport models to validate covariance, convergence, conditioning dependence, and correction fidelity.
Quantum optical synthesis of high-dimensional ultrafast frequency-bin qudits
Graduate School of Informatics and Engineering, The University of Electro-Communications（电子通信大学信息工程研究生院）；Advanced ICT Research Institute, National Institute of Information and Communications Technology（国家信息通信技术研究所先进ICT研究所）；Institute for Advanced Science, The University of Electro-Communications（电子通信大学高等科学研究院）
Qudit extension of parameterized IQP circuits: A generative quantum machine learning approach to integer data
Parity Quantum Computing Germany GmbH（Parity量子计算德国有限公司）；Parity Quantum Computing GmbH（Parity量子计算有限公司）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）
Photonic quantum information with time-bins: Principles and applications
University of Calgary（卡尔加里大学）；California Institute of Technology（加州理工学院）；John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）
Institute for Advancing Intelligence, TCG CREST（TCG CREST 推进智能研究所）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学量子信息与计算科学联合中心）
