Sequential Measurements, Topological Quantum Field Theories, and Topological Quantum Neural Networks

• DOI: 10.1002/prop.202200104
• Publication Date: 2022-09-02T21:20:57Z
• Authors: Chris Fields; James F. Glazebrook; Antonino Marcianò
• Keywords: 0101 mathematics; 01 natural sciences

Abstract We introduce novel methods for implementing generic quantum information within a scale‐free architecture. For given observable system, we show how observational outcomes are taken to be finite bit strings induced by measurement operators derived from holographic screen bounding the system. In this framework, measurements of identified systems with respect defined reference frames represented semantically‐regulated flows through distributed sets binary‐valued Barwise‐Seligman classifiers. Specifically, construct functor category cone‐cocone diagrams (CCCDs) over classifiers, cobordisms Hilbert spaces. that CCCDs provide representation (QRFs). Hence constructed shows sequential can induce TQFTs. The only requirement is each in sequence, itself, satisfies Bayesian coherence, hence probabilities it assigns satisfy Kolmogorov axioms. extend analysis too develop topological neural networks (TQNNs), which enable machine learning functorial evolution 2‐complexes (TQN2Cs) governed TQFTs amplitudes, and resort Atiyah‐Singer theorems order classify data processed TQN2Cs. then comment about quiver generalized spin‐networks, basis spaces both TQNNs finally review potential implementations framework solid state physics suggest applications simulation biological processing.