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Fractal-Curvature Photonic Qubit: Self-Similar Geometry as Magnetic-Field-Free Topological Protection

PREZAT, PASCAL

Published Nov 19, 2025• 0 citations
Publisher

Abstract

We introduce a topological qubit encoded in the curvature of a polariton supersolid imprinted onto a self-similar fractal mirror (Hausdorff dimension 2.3). The effective quantum metric inherits the fractal spectrum, yielding a power-law decoherence rate Γeff(L) = ηΓ0(L/L0)−0.48. Combined with bi-split laser echo and undetected twin-photon management we predict T2 ≥ 12ms and two-qubit gate fidelity F ≥ 99.97% at 4K without external magnetic field. The whole stack is CMOS-back-end compatible and deployable on silicon-photonic or free-space military links.

DOI
10.5281/zenodo.17654425

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We introduce a topological qubit encoded in the curvature of a polariton supersolid imprinted onto a self-similar fractal mirror (Hausdorff dimension 2.3). The effective quantum metric inherits the fractal spectrum, yielding a power-law decoherence rate Γeff(L) = ηΓ0(L/L0)−0.48. Combined with bi-split laser echo and undetected twin-photon management we predict T2 ≥ 12ms and two-qubit gate fidelity F ≥ 99.97% at 4K without external magnetic field. The whole stack is CMOS-back-end compatible and deployable on silicon-photonic or free-space military links.
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The field of topological photonics leverages concepts from geometry and topology – the branch of mathematics that deals with global properties that cannot be changed under continuous deformation – to produce electromagnetic modes that propagate with immunity to certain types of disorder and imperfections. In the last few years, several experiments have achieved the generation and propagation of quantum states of light in these so-called topological modes, demonstrating enhanced robustness of such inherently fragile quantum states. In this talk we will focus on our recent results in this area including topological protection of spatial entanglement and the demonstration of topology as an additional degree of freedom for entanglement using CMOS-compatible silicon photonics platforms.
This paper proposes a novel framework for quantum information processing rooted in the principles of fractal geometry. The core claim is that the dimensionality of quantum systems can be inherently linked to fractal structures, offering a fundamentally new approach to data storage and computation. We investigate the utilization of fractal patterns to encode quantum states, exploiting the enhanced information density and computational potential afforded by fractal geometry. Specifically, we explore methods for representing and manipulating quantum states within fractal spaces, utilizing concepts such as self-similarity and non-integer dimensions. The theoretical framework presented demonstrates a potential pathway to significantly increased storage capacity and more efficient quantum algorithms. The key innovation lies in the direct mapping of quantum information onto fractal landscapes, which promises to unlock new possibilities in quantum technologies. The exploration includes examining different fractal types (e.g., Mandelbrot set, Sierpinski triangle) and their suitability for specific quantum information tasks. The research highlights the potential for designing quantum systems with intrinsic fractal properties, leading to enhanced robustness and scalability. Ultimately, this work aims to establish a foundational understanding of how fractal geometry can be leveraged to revolutionize quantum information processing.
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We present the Quantized Fractal Equation (QFE) framework[1] for quantum open systems (QFEXIII), providing a novel, purely deterministic and geometric alternative to the traditional Copenhagen interpretation of wave-packet collapse. By replacing the subjective intervention of a consciousobserver with the non-local topological friction of a variable-order fractal[9] spacetime, we formalizethe mechanism of quantum decoherence from first principles. We construct the generalized QFEFractional Master Equation, wherein the multi-field interactions under environmental scattering actas localized excitations of the spacetime torsion tensor within ́Elie Cartan’s geometry[2]. We rigorously demonstrate that the resulting geometric torsion anomaly is dynamically self-screened on thepurified physical Hilbert space, triggering an autonomous, power-law dampening of quantum coherences