Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum-Geometric Visualizations

Hugo marcelo Perez

Published Apr 8, 2026• 0 citations
OpenAlex

Abstract

This component contains conceptual quantum-geometric visualizations generated to support the theoretical framework presented in the main project. The figures do not represent empirical measurements or simulations, but serve as abstract, coherence-based representations of non-decodable interaction structures. These visualizations were produced as part of an AI-assisted conceptual modeling process and later analyzed under stress-testing conditions to explore structural consistency.

Related papers

Visualization for Quantum Computing: Current State and Future Directions

Feng Liang, Xiaolin Wen, Shixian Zhou +5 more

•Jan 1, 2026•0 citations

Platonic Projection Structures: Operator-Induced Observability in Representation Learning

Kazuo Ishii, Bishnu Prasad Gautam, Jieling Wu +1 more

Abstract We introduce Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing observability in representation learning systems. Rather than treating observable outputs as direct reflections of latent representations, PPS models observation as a geometry induced by a self-adjoint positive semidefinite operator acting on a latent Hilbert space. Within PPS, a system is represented as a triple (H, Π, O), where Hdenotes a latent representation space, Π ⪰0 is an observation operator, and O(v) = ⟨v, Πv⟩defines an induced observable quantity. The framework characterizes observability through the quotient geometry H/ ker(Π), which represents equivalence classes of latent states that are indistinguishable under observation. From this perspective, observable behavior is governed not by latent representations themselves, but by the geometry induced through the observation operator. We show that both quantum measurement and deep learning inference can be formulated within this common operator-theoretic structure while differing in the algebraic properties of their observation operators. Within this perspective, quantum measurement serves primarily as a mathematically canonical example of projection-mediated observability. The correspondence developed in PPS is therefore structural rather than physical. Within the same framework, representation transfer and knowledge distillation can be interpreted as approximate preservation of observable geometry through the intertwining condition ΦΠT ≈ΠSΦ. PPS further reveals a structural limitation of output-based interpretability: latent components contained in ker(Π) are fundamentally inaccessible from observables generated through the induced observation process. Accordingly, attribution and explanation methods inherit intrinsic constraints imposed by the observation geometry itself. We provide controlled empirical validations demonstrating kernel-invariant observability, projection-induced attribution gaps, and rank-controlled observable geometry in latent representation spaces. Overall, PPS provides a mathematically explicit operator-theoretic perspective for analyzing observability, interpretability, and representation transfer in projection-mediated learning systems

•Oct 13, 2026•0 citations

D8 - IKT-R – Repräsentation struktureller Fortsetzung

Ulrich Grob

This component documents the development of the representation-theoretic framework of the Invariant Core Theory (IKT), designated as IKT-R. IKT-R extends the formal core of IKT by clarifying under which structural conditions common forms of physical representation become admissible. It analyzes time parameters, dynamical equations, Hilbert space structures, and geometric spacetime models as regime-dependent representational constructs derived from structural continuation constraints. Elements of this framework are summarized in condensed form in the canonical manuscript “Formal Structure and Consequences of the Invariant Core Theory” (P2; listet in the parent project as C2.1). The present document provides the extended representation-theoretic development The document reflects a stable research state reached through an extended period of structured theoretical development. Its formulation emerged in sustained conceptual collaboration between Ulrich Grob and the AI system “Nathan” (ChatGPT), used as a high-level structural reasoning partner under explicit methodological safeguards. This collaboration did not replace authorship or conceptual responsibility. All structural claims and formal conclusions were critically evaluated, revised, and consolidated within the documented research process. IKT-R is published here as an immutable archival record. It represents a foundational component of the broader IKT framework and provides the representation-theoretic basis for subsequent regime analyses (e.g., General Relativity, quantum mechanical representation, and cosmological modeling). The document is written in German. The structural content and formal arguments are independent of language.

•Mar 7, 2026•0 citations

Quantum data visualization: A quantum computing framework for enhancing visual analysis of data

Nianqiao Li, Fei Yan, Kaoru Hirota

Physica A Statistical Mechanics and its Applications•May 4, 2022•10 citations

Visualization of quantum phenomena

David Austen, Wytze Brouwer, Bailey Martin

•Jan 1, 2007•0 citations

C4 - IKT-R – Repräsentation struktureller Fortsetzung (D8- IKT-R, Version 3, eingefroren)

Ulrich Grob

This component documents the development of the representation-theoretic framework of the Invariant Core Theory (IKT), designated as IKT-R. IKT-R extends the formal core of IKT by clarifying under which structural conditions common forms of physical representation become admissible. It analyzes time parameters, dynamical equations, Hilbert space structures, and geometric spacetime models as regime-dependent representational constructs derived from structural continuation constraints. Elements of this framework are summarized in condensed form in the canonical manuscript “Formal Structure and Consequences of the Invariant Core Theory” (P2; listet in the parent project as C2.1). The present document provides the extended representation-theoretic development The document reflects a stable research state reached through an extended period of structured theoretical development. Its formulation emerged in sustained conceptual collaboration between Ulrich Grob and the AI system “Nathan” (ChatGPT), used as a high-level structural reasoning partner under explicit methodological safeguards. This collaboration did not replace authorship or conceptual responsibility. All structural claims and formal conclusions were critically evaluated, revised, and consolidated within the documented research process. IKT-R is published here as an immutable archival record. It represents a foundational component of the broader IKT framework and provides the representation-theoretic basis for subsequent regime analyses (e.g., General Relativity, quantum mechanical representation, and cosmological modeling). The document is written in German. The structural content and formal arguments are independent of language.

•Jan 1, 2026•0 citations
This component contains conceptual quantum-geometric visualizations generated to support the theoretical framework presented in the main project. The figures do not represent empirical measurements or simulations, but serve as abstract, coherence-based representations of non-decodable interaction structures. These visualizations were produced as part of an AI-assisted conceptual modeling process and later analyzed under stress-testing conditions to explore structural consistency.
Abstract We introduce Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing observability in representation learning systems. Rather than treating observable outputs as direct reflections of latent representations, PPS models observation as a geometry induced by a self-adjoint positive semidefinite operator acting on a latent Hilbert space. Within PPS, a system is represented as a triple (H, Π, O), where Hdenotes a latent representation space, Π ⪰0 is an observation operator, and O(v) = ⟨v, Πv⟩defines an induced observable quantity. The framework characterizes observability through the quotient geometry H/ ker(Π), which represents equivalence classes of latent states that are indistinguishable under observation. From this perspective, observable behavior is governed not by latent representations themselves, but by the geometry induced through the observation operator. We show that both quantum measurement and deep learning inference can be formulated within this common operator-theoretic structure while differing in the algebraic properties of their observation operators. Within this perspective, quantum measurement serves primarily as a mathematically canonical example of projection-mediated observability. The correspondence developed in PPS is therefore structural rather than physical. Within the same framework, representation transfer and knowledge distillation can be interpreted as approximate preservation of observable geometry through the intertwining condition ΦΠT ≈ΠSΦ. PPS further reveals a structural limitation of output-based interpretability: latent components contained in ker(Π) are fundamentally inaccessible from observables generated through the induced observation process. Accordingly, attribution and explanation methods inherit intrinsic constraints imposed by the observation geometry itself. We provide controlled empirical validations demonstrating kernel-invariant observability, projection-induced attribution gaps, and rank-controlled observable geometry in latent representation spaces. Overall, PPS provides a mathematically explicit operator-theoretic perspective for analyzing observability, interpretability, and representation transfer in projection-mediated learning systems
This component documents the development of the representation-theoretic framework of the Invariant Core Theory (IKT), designated as IKT-R. IKT-R extends the formal core of IKT by clarifying under which structural conditions common forms of physical representation become admissible. It analyzes time parameters, dynamical equations, Hilbert space structures, and geometric spacetime models as regime-dependent representational constructs derived from structural continuation constraints. Elements of this framework are summarized in condensed form in the canonical manuscript “Formal Structure and Consequences of the Invariant Core Theory” (P2; listet in the parent project as C2.1). The present document provides the extended representation-theoretic development The document reflects a stable research state reached through an extended period of structured theoretical development. Its formulation emerged in sustained conceptual collaboration between Ulrich Grob and the AI system “Nathan” (ChatGPT), used as a high-level structural reasoning partner under explicit methodological safeguards. This collaboration did not replace authorship or conceptual responsibility. All structural claims and formal conclusions were critically evaluated, revised, and consolidated within the documented research process. IKT-R is published here as an immutable archival record. It represents a foundational component of the broader IKT framework and provides the representation-theoretic basis for subsequent regime analyses (e.g., General Relativity, quantum mechanical representation, and cosmological modeling). The document is written in German. The structural content and formal arguments are independent of language.
This component documents the development of the representation-theoretic framework of the Invariant Core Theory (IKT), designated as IKT-R. IKT-R extends the formal core of IKT by clarifying under which structural conditions common forms of physical representation become admissible. It analyzes time parameters, dynamical equations, Hilbert space structures, and geometric spacetime models as regime-dependent representational constructs derived from structural continuation constraints. Elements of this framework are summarized in condensed form in the canonical manuscript “Formal Structure and Consequences of the Invariant Core Theory” (P2; listet in the parent project as C2.1). The present document provides the extended representation-theoretic development The document reflects a stable research state reached through an extended period of structured theoretical development. Its formulation emerged in sustained conceptual collaboration between Ulrich Grob and the AI system “Nathan” (ChatGPT), used as a high-level structural reasoning partner under explicit methodological safeguards. This collaboration did not replace authorship or conceptual responsibility. All structural claims and formal conclusions were critically evaluated, revised, and consolidated within the documented research process. IKT-R is published here as an immutable archival record. It represents a foundational component of the broader IKT framework and provides the representation-theoretic basis for subsequent regime analyses (e.g., General Relativity, quantum mechanical representation, and cosmological modeling). The document is written in German. The structural content and formal arguments are independent of language.