A Gauge-Covariant Theoretical Framework for Non-Abelian Holonomy Estimation and Feed-Forward Correction in Time-Bin Photonic Qudits

• URL: http://arxiv.org/abs/2605.26697v1
• Date: Tue, 26 May 2026 08:40:26 GMT
• Title: A Gauge-Covariant Theoretical Framework for Non-Abelian Holonomy Estimation and Feed-Forward Correction in Time-Bin Photonic Qudits
• Abstract summary: We develop a theoretical framework for estimating and correcting non-Abelian geometric distortions in time-bin photonic qudit processing.<n>The work does not assume a device-specific transfer matrix, loss model, detector model, or experimental calibration pipeline.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• A Commutator Framework for Selective Spectral Alignment in Deep Neural Networks [0.0]
  We develop a finite-width geometric framework describing how learned feature geometries are organized, transported, and selectively aligned in deep neural networks.<n>Incompatibility among weight-generated covariance, gates, and backward sensitivities is quantified through three families of commutators.<n>We establish spectral-gap, projector-evolution, and stabilization estimates, and formulate conditional Lyapunov principles that yield decay under explicit geometric error-bound or intrinsic-damping assumptions.
  arXiv  Detail & Related papers  (2026-08-24T07:42:16Z)
• Representation-Induced Symmetry Trapping in Adaptive Variational Quantum Simulations of Multi-Reference Topologies [0.0]
  We evaluate a spin-conserved SUSD operator pool across highly stretched configurations.<n>We show that the preservation of point-group symmetry structurally protects the optimization landscape.<n> exploiting structural overlap within our pool, we introduce a co-variance-driven, adaptive shot-allocation filter.
  arXiv  Detail & Related papers  (2026-06-11T14:16:11Z)
• Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration [71.51826063983434]
  Image restoration is an inherently ill posed inverse problem.<n>We use non strict symmetry as a constraint to formulate the restoration inverse problem.<n>We show that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size.
  arXiv  Detail & Related papers  (2026-05-13T16:22:19Z)
• Gauge-Equivariant Intrinsic Neural Operators for Geometry-Consistent Learning of Elliptic PDE Maps [0.0]
  We propose Gauge-Equivariant Intrinsic Neural Operators (GINO) for geometric partial differential equations (PDEs)<n>GINO parameterize elliptic solution maps through intrinsic spectral multipliers acting on geometry-dependent spectra, coupled with gauge-equivariant nonlinearities.<n>We show GINO achieves low operator-approximation error, near machine-precision gauge equivariance, equi robustness to structured metric perturbations, strong cross-resolution generalization with small commutation error under restriction/prolongation, and structure-preserving performance on a regularized exact/coexact decomposition task.
  arXiv  Detail & Related papers  (2026-03-16T02:10:06Z)
• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• ODELoRA: Training Low-Rank Adaptation by Solving Ordinary Differential Equations [54.886931928255564]
  Low-rank adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning method in deep transfer learning.<n>We propose a novel continuous-time optimization dynamic for LoRA factor matrices in the form of an ordinary differential equation (ODE)<n>We show that ODELoRA achieves stable feature learning, a property that is crucial for training deep neural networks at different scales of problem dimensionality.
  arXiv  Detail & Related papers  (2026-02-07T10:19:36Z)
• ARGUS: Adaptive Rotation-Invariant Geometric Unsupervised System [0.0]
  This paper introduces Argus, a framework that reconceptualizes drift detection as tracking local statistics over a fixed spatial partition of the data manifold.<n> Voronoi tessellations over canonical orthonormal frames yield drift metrics that are invariant to transformations.<n>A graph-theoretic characterization of drift propagation is developed that distinguishes coherent distributional shifts from isolated perturbations.
  arXiv  Detail & Related papers  (2026-01-03T22:39:20Z)
• Neural Optimal Transport Meets Multivariate Conformal Prediction [58.43397908730771]
  We propose a framework for conditional vectorile regression (CVQR)<n>CVQR combines neural optimal transport with quantized optimization, and apply it to predictions.
  arXiv  Detail & Related papers  (2025-09-29T19:50:19Z)
• Euclidean Distance Matrix Completion via Asymmetric Projected Gradient Descent [25.846262685970164]
  This paper proposes and analyzes a gradient-type algorithm based on Burer-Monteiro factorization.<n>It reconstructs the point set configuration from partial Euclidean distance measurements.
  arXiv  Detail & Related papers  (2025-04-28T07:13:23Z)
• Stable Nonconvex-Nonconcave Training via Linear Interpolation [51.668052890249726]
  This paper presents a theoretical analysis of linearahead as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear can help by leveraging the theory of nonexpansive operators.
  arXiv  Detail & Related papers  (2023-10-20T12:45:12Z)
• Spectrum-Aware Debiasing: A Modern Inference Framework with Applications to Principal Components Regression [1.342834401139078]
  We introduce SpectrumAware Debiasing, a novel method for high-dimensional regression. Our approach applies to problems with structured, heavy tails, and low-rank structures. We demonstrate our method through simulated and real data experiments.
  arXiv  Detail & Related papers  (2023-09-14T15:58:30Z)
• Last-Iterate Convergence of Adaptive Riemannian Gradient Descent for Equilibrium Computation [52.73824786627612]
  This paper establishes new convergence results for textitgeodesic strongly monotone games.<n>Our key result shows that RGD attains last-iterate linear convergence in a textitgeometry-agnostic fashion.<n>Overall, this paper presents the first geometry-agnostic last-iterate convergence analysis for games beyond the Euclidean settings.
  arXiv  Detail & Related papers  (2023-06-29T01:20:44Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.