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728 papers from the QNFO program, filed on nine shelves by the reader each one is written for: energy per answer, error correction, physics, numbers and p-adics, logic and formalism, AI and knowledge, autonomous systems, assessments, and cross-cutting essays. Every page renders its mathematics and can be questioned in place. How a living paper works.
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Results for “topological” 6 papers
Fault‑Tolerant Quantum Memory as a Thermodynamic Phase in a 4‑D Topological Photonic Lattice
Passive protection of quantum information can be achieved when a material phase possesses a bulk energy gap that exceeds the ambient thermal energy. Existing self‑correcting memory proposals rely on many‑body Hamiltonians that are difficult to engineer. We propose a concrete photonic implementation…
Falsifying Geometrically Inspired Quantum Error‑Correcting Codes via Distinct Logical‑Error Scaling
Geometric constructions of quantum error‑correcting codes (QECCs) have been proposed as alternatives to standard topological codes, yet their physical relevance remains ambiguous. Existing proposals lack a testable prediction that distinguishes them from surface‑code scaling of logical error rates.…
Deductive Verification of Discrete‑Time Quantum‑Walk Simulators: Contracts, Cost Bounds, and Extensions to Graph‑Generalized and Open‑System Walks
Discrete‑time quantum walks are a universal model of quantum computation, a platform for topological phases, and a testbed for quantum algorithms, yet the simulators used to study them are rarely checked with the rigor applied to classical library code. This paper frames quantum‑walk simulator…
Adelic Quantum Error Correction: A Synthesis Across All Primes v1.0.0
The $p$-adic quantum error correction program has developed three independent but connected strands: a mathematical theory of $p$-adic stabilizer codes (Phase A), an experimental protocol to test for ultrametric error structure (Phase B), and a hardware co-design proposal for tree-structured qubit…
Adelic Quantum Error Correction: Intrinsic Qubit Protection from Ostrowski
We formalize an adelic approach to quantum error correction (QEC) based on Ostrowski's theorem: the only non-trivial completions of the rational numbers are the Archimedean (real) completion $\mathbb{R}$ and the p-adic completions $\mathbb{Q}_p$, and these topologies are mutually singular. The…
Phase Transitions of Logic
The realization of fault-tolerant universal quantum computation is currently hindered by a fundamental dichotomy between substrate controllability and intrinsic robustness. This paper introduces the “Universal Hamiltonian Computational Substrate” (UHCS) framework to quantitatively compare two…
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