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

The Axioms of Quantum Field Theory, Quantum Variational Calculus, Quantum Logic Theory, Quantum Computability, Quantum Computational Complexity and Quantum Geometric Algebra

Daniel Cordero Grau

Published Jul 1, 2016• 0 citations
OpenAlex

Related papers

Topological Elevation of Intuitionistic Logic and the Axiomatic Foundation of Univalent Rough Operator Algebra (UROA)

Seonggil Lee

This paper establishes a unified meta-mathematical foundation for quantum gravity by elevating intuitionistic logic through Homotopy Type Theory (HoTT) and merging it with Rough Operator Algebra (ROA) [2, 3]. We address the limitations of classical logic and standard intuitionism in modeling quantum superposition and continuous topologies. By formally equating quantum entanglement with topological paths via the Univalent ER = EPR Axiom, we construct the Univalent Rough Operator Algebra (UROA) framework. Furthermore, we prove the logical consistency of this framework against the monogamy of entanglement bymapping it to higher-dimensional simplices (GHZ states), and formulate the core integration theorems of the Seonggil Field Equations (SFE) [1] and Seonggil Tensor Calculus (STCT)[4].

•Sep 20, 2026•0 citations

Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints

Albert S. Schwarz

SpringerBriefs in physics•Jan 1, 2024•2 citations

Computational Complexity Theory of Quantum Turing Machines and Quantum Circuits

Harumichi Nishimura, 治道 西村

•Mar 26, 2001•1 citation

FBGT:Arithmetic Quantum Entanglement and P ≠ NP(2)

xun zhang

"Knowledge belongs to all humanity.""A paper only marks the directions and places where human mathematicians have explored and once arrived." FBGT: Arithmetic Quantum Entanglement and P ≠ NP (v1)Published September 24, 2026 | Preprint | OpenAuthor: Zhang Xun | ORCID: 0009-0004-5396-8952 | CC BY 4.0 Cryptographic Seal (Original Manuscript SHA-256):FBEC4F182B81F5A5368CA21E143019A75CCA606DFB74926249B2589755C0C73C This repository hosts Cognitive Topology, a framework bridging differential geometry, algebraic geometry, category theory, quantum information, and computational complexity. Core Thesis: Traditional complexity theory asks whether shortcuts exist in a flat, discrete combinatorial space. This work asks: What is the geometric cost of dimensional projection? By introducing the Cognitive Manifold, Observer Endofunctors, Arithmetic Scale Bundles, and the Boundary Obstruction Class O_{P/NP}, it argues that computational complexity is intrinsically geometric. P ≠ NP follows from the non-vanishing topological curvature of higher-dimensional fiber bundles projected onto lower-dimensional spaces. Novel Discovery: Quantum entanglement reduces to the algorithmic rigidity of arithmetic scale operators. Decimal multiplication (e.g., 4 × 2.1) is a dimensional lifting and projection process: extract integer skeletons (A, B) and scale exponents (m, n); perform pure integer multiplication A × B in high-dimensional integer space; then project back via the rigid exponent addition rule 10^(−(m+n)). This is isomorphic to the preparation and measurement of an entangled quantum state. Quantum non-locality is thus not “spooky action at a distance,” but a holographic projection of higher-dimensional curvature onto lower-dimensional arithmetic spaces. Key Pillars: Cognitive Manifold & Axioms: Axiom A0 places the observer inside the system; Axiom A3 (Boundary Convergence) geometrically resolves Gödel’s Incompleteness. Algorithmic Rigidity & Adjoint Functors: Lifting (Extension) and projection (Restriction) obey strict adjunctions E ⊣ R. Logic is geometry. Arithmetic as Algebraic Spectrum: Decimal multiplication is a discrete projection of algebraic spectrum theory. Quantum Entanglement as Fiber Bundle Curvature: Non-locality is the holographic projection of higher-dimensional gauge curvature. Geometric P ≠ NP: The boundary obstruction class O_{P/NP} is non-trivial; no polynomial-time algorithm can flatten the topological residue of high-dimensional algebraic varieties. The framework Version v410.5281/zenodo.22533545 Sep 6, 2026 Version v310.5281/zenodo.21618022 Jul 27, 2026 Version v210.5281/zenodo.21614404 Jul 27, 2026 Version v110.5281/zenodo.21595680 Jul 26, 2026

•Sep 24, 2026•0 citations

Linear-algebraic Lambda-calculus: higher-order, encodings and confluence

Pablo J. Arrighi, Gilles Dowek B

We introduce a minimal language combining both higher-order computation and linear algebra. Roughly, this is nothing else than the Lambda-calculus together with the possibility to make linear combinations of terms a.t+b.u. We describe how to "execute" this language in terms of a few rewrite rules, and justify them through the two fundamental requirements that the language be a language of linear operators, and that it be higher-order. We mention the perspectives of this work in field of quantum computation, which we show can be easily encoded in the calculus, as well as in other domains such as the interpretation of linear logic. Finally we prove the confluence of the calculus, this is our main result. Keywords: quantum programming language, quantum control, quantum logic, probabilistic and quantitative analysis, rewriting techniques.

•Dec 22, 2006•30 citations

Quantum Theory in Algebraic and Geometric Approaches

Albert S. Schwarz

SpringerBriefs in physics•Jan 1, 2024•0 citations
This paper establishes a unified meta-mathematical foundation for quantum gravity by elevating intuitionistic logic through Homotopy Type Theory (HoTT) and merging it with Rough Operator Algebra (ROA) [2, 3]. We address the limitations of classical logic and standard intuitionism in modeling quantum superposition and continuous topologies. By formally equating quantum entanglement with topological paths via the Univalent ER = EPR Axiom, we construct the Univalent Rough Operator Algebra (UROA) framework. Furthermore, we prove the logical consistency of this framework against the monogamy of entanglement bymapping it to higher-dimensional simplices (GHZ states), and formulate the core integration theorems of the Seonggil Field Equations (SFE) [1] and Seonggil Tensor Calculus (STCT)[4].
"Knowledge belongs to all humanity.""A paper only marks the directions and places where human mathematicians have explored and once arrived." FBGT: Arithmetic Quantum Entanglement and P ≠ NP (v1)Published September 24, 2026 | Preprint | OpenAuthor: Zhang Xun | ORCID: 0009-0004-5396-8952 | CC BY 4.0 Cryptographic Seal (Original Manuscript SHA-256):FBEC4F182B81F5A5368CA21E143019A75CCA606DFB74926249B2589755C0C73C This repository hosts Cognitive Topology, a framework bridging differential geometry, algebraic geometry, category theory, quantum information, and computational complexity. Core Thesis: Traditional complexity theory asks whether shortcuts exist in a flat, discrete combinatorial space. This work asks: What is the geometric cost of dimensional projection? By introducing the Cognitive Manifold, Observer Endofunctors, Arithmetic Scale Bundles, and the Boundary Obstruction Class O_{P/NP}, it argues that computational complexity is intrinsically geometric. P ≠ NP follows from the non-vanishing topological curvature of higher-dimensional fiber bundles projected onto lower-dimensional spaces. Novel Discovery: Quantum entanglement reduces to the algorithmic rigidity of arithmetic scale operators. Decimal multiplication (e.g., 4 × 2.1) is a dimensional lifting and projection process: extract integer skeletons (A, B) and scale exponents (m, n); perform pure integer multiplication A × B in high-dimensional integer space; then project back via the rigid exponent addition rule 10^(−(m+n)). This is isomorphic to the preparation and measurement of an entangled quantum state. Quantum non-locality is thus not “spooky action at a distance,” but a holographic projection of higher-dimensional curvature onto lower-dimensional arithmetic spaces. Key Pillars: Cognitive Manifold & Axioms: Axiom A0 places the observer inside the system; Axiom A3 (Boundary Convergence) geometrically resolves Gödel’s Incompleteness. Algorithmic Rigidity & Adjoint Functors: Lifting (Extension) and projection (Restriction) obey strict adjunctions E ⊣ R. Logic is geometry. Arithmetic as Algebraic Spectrum: Decimal multiplication is a discrete projection of algebraic spectrum theory. Quantum Entanglement as Fiber Bundle Curvature: Non-locality is the holographic projection of higher-dimensional gauge curvature. Geometric P ≠ NP: The boundary obstruction class O_{P/NP} is non-trivial; no polynomial-time algorithm can flatten the topological residue of high-dimensional algebraic varieties. The framework Version v410.5281/zenodo.22533545 Sep 6, 2026 Version v310.5281/zenodo.21618022 Jul 27, 2026 Version v210.5281/zenodo.21614404 Jul 27, 2026 Version v110.5281/zenodo.21595680 Jul 26, 2026
We introduce a minimal language combining both higher-order computation and linear algebra. Roughly, this is nothing else than the Lambda-calculus together with the possibility to make linear combinations of terms a.t+b.u. We describe how to "execute" this language in terms of a few rewrite rules, and justify them through the two fundamental requirements that the language be a language of linear operators, and that it be higher-order. We mention the perspectives of this work in field of quantum computation, which we show can be easily encoded in the calculus, as well as in other domains such as the interpretation of linear logic. Finally we prove the confluence of the calculus, this is our main result. Keywords: quantum programming language, quantum control, quantum logic, probabilistic and quantitative analysis, rewriting techniques.