Ultrametric Quantum Computing

Replacing Archimedean geometry with ultrametric geometry for quantum computing. The Bruhat-Tits tree — a structure from p-adic number theory — provides passive error suppression through the strong triangle inequality, operating at 4 K with no active error correction. This portal links all QNFO quantum research: foundational papers, computational evidence, interactive demos, and the full 498-paper catalog.

Core Papers See Evidence Explore Demos 498 Papers

Core Ultrametric Quantum Papers

Foundational research across quantum computation, field theory, geometry, and AI

Ultrametric Quantum Computation and the Langlands Program

quantum.qnfo.org

Connects ultrametric quantum computing architecture to the geometric Langlands program. Neutral atom hardware specification, ternary tree circuits, 48× error reduction.

Paper

The Ultrametric Paradigm

paradigm.qnfo.org

Establishes ultrametric geometry as a unifying framework across physics, computation, and cognition. The foundational paradigm paper.

Framework

Ultrametricity — The Unity of Ultrametric Physics

unity.qnfo.org

18-chapter book deriving quantum mechanics, QFT, gravity, and the Standard Model from ultrametric geometry. Includes quantum computation chapter.

Book

Quantum Laws of Form

laws.qnfo.org

Syntactic foundation for physics. Derives quantum mechanics from formal language constraints using Spencer-Brown’s calculus of indications.

Framework

Adelic Constraints on Quantum Field Theory

adelic.qnfo.org

Applies adelic number theory to constrain QFT constructions. Connects Archimedean and non-Archimedean places.

Paper

The Hierarchical Universe

hierarchy.qnfo.org

How one geometric structure unifies numbers, computation, physics, and meaning — and how to build machines that live within it.

Framework

Different Physics

different.qnfo.org

Explores the consequences of switching from Archimedean to ultrametric geometry as the foundational mathematical structure of physics.

Paper

Two Ways of Measuring

measure.qnfo.org

Comparative analysis of Archimedean vs. ultrametric distance measures and their physical implications.

Paper

Ultrametric AI — Proof of Concept

ai-poc.qnfo.org

Demonstrates glass-box AI architectures using ultrametric tree structures. Q-PNA linear mapping with cophenetic loss.

AI

Computational Evidence

Tier 0–1 computational validation across Bruhat-Tits tree encoding and glass-box AI architectures

0
Zero Logical Errors at depth 7 (2,187 leaves) with physical error rates up to 40%
48×
Logical error reduction encoding one bit across q=128 leaves — zero additional qubit cost
40
Neutral atom hardware specification: ternary tree depth 3, Rydberg blockade, 4 K operation
6.6×
Glass-box AI advantage over transformer on hierarchical classification. 100% STC detection

Explore the Ecosystem

Interactive tools, Q&A oracle, and the full research corpus

QWAV Technical Hub

Evidence dashboard, core publications, interactive demos, and development roadmap.

Papers Catalog

498 open-access papers on ultrametric quantum computing, geometric physics, and glass-box AI. Search by title or keyword.

Ask QWAV

Research Q&A oracle. Queries the full corpus with evidence-backed answers. 949 vectors indexed.

QLOF Primer

Interactive knowledge graph and guided tour through Quantum Laws of Form concepts.

QNFO Research Archive

Complete archive of all QNFO publications, datasets, and supplementary materials.

Infrastructure Directory

Full directory of all QWAV/QNFO sites, tools, and services across the ecosystem.