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Modules
QWAV's technical framework is organized into 12 mathematical modules. Each module addresses a specific aspect of ultrametric quantum physics.
Establishes the mathematical framework for ultrametric valuations. Defines ratio-based encoding where physical qubits carry valuation ratios that encode their position in the hierarchical tree structure.
Constructs the Bruhat-Tits tree — the central geometric object of QWAV. This infinite regular tree encodes the structure of p-adic numbers and provides the geometric substrate for ultrametric quantum computation.
Defines the Vladimirov operator — the p-adic analog of the Laplace operator. This operator governs dynamics on ultrametric spaces, analogous to how the Laplacian governs dynamics in Euclidean quantum mechanics.
Extends the framework to adelic spaces, unifying behavior across all primes simultaneously. Provides a complete description of quantum states on ultrametric spaces using adelic methods from number theory.
Implements quantum error correction using the ratio-based encoding from M1. Errors are confined to individual branches of the Bruhat-Tits tree, providing intrinsic fault tolerance without active syndrome measurement.
Defines quantum gates that operate on ultrametric-encoded qubits. Gates respect the tree's hierarchical structure, ensuring that operations on one branch do not disturb others.
Analyzes the thermodynamic limits of ultrametric quantum computation. Derives scaling laws for energy, entropy, and computational capacity as functions of tree depth and branching factor.
Applies the Wheeler-DeWitt equation to ultrametric quantum geometries. Investigates quantum gravitational aspects of tree-based computation, connecting to quantum cosmology.
Demonstrates that Lorentz symmetry emerges naturally from the ultrametric structure at appropriate scales. The continuous spacetime of special relativity arises as a limiting case of the underlying discrete tree geometry.
Explores cosmological implications of ultrametric quantum physics. Investigates how tree-based geometries might inform our understanding of early-universe physics and cosmic structure formation.
Defines the Monna map — a mapping between p-adic and real numbers that connects ultrametric and Euclidean descriptions. Provides a bridge between tree-based and continuous mathematical frameworks.
Integrates all modules into a unified framework. Demonstrates the consistency and completeness of the ultrametric quantum computing paradigm across all 11 preceding modules.
- Architecture — How modules fit together
- Publications — Module-specific publications
- Source Code — Full mathematical development