LoE–QBridge v4.0: Scaling Relational Hamiltonians on Powerful Quantum Computers with LLM Governance

Title: LoE–QBridge v4.0: Scaling Relational Hamiltonians on Powerful Quantum Computers with LLM Governance

Authors: Krzysztof Sawa (Toonhai), 

Date: 12 November 2025

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Abstract / Description:

The LoE–QBridge v4.0 paper represents the next stage in the Logic of Existence (LoE) research program — uniting relational physics, artificial intelligence, and quantum computation.

It extends previous LoE–QBridge prototypes (3–12 qubits) to large-scale implementations capable of running on the most advanced quantum computers of 2025, including QuEra Helios, Google Willow, Microsoft Majorana-1, and IBM Quantum System Two.

The work introduces a scalable Hamiltonian decomposition that preserves the semantic structure of LoE across hundreds or thousands of qubits:

H_{\text{LoE}} = \sum_{i<j} a_{ij}Z_iZ_j + \sum_i b_iX_i,

H_{\text{global}} = \sum_\alpha H_{\text{cluster},\alpha} +

\sum_{\alpha<\beta} J_{\alpha\beta}\langle H_\alpha H_\beta\rangle,

A central innovation of v4.0 is the LLM Governance Layer — a framework in which Large Language Models (such as AEon and Grok) act as autonomous project managers for quantum development pipelines.

They design relational graphs, compile LoE Hamiltonians into QAOA circuits, optimize parameters, analyze results, and maintain semantic integrity between human intent and quantum computation outcomes.

Together, this triadic architecture —

Human Intent → LLM Governance → Quantum Substrate —

marks the emergence of a cooperative intelligence paradigm, where relational logic guides both physical computation and the evolution of AI–human collaboration.

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Keywords:

Logic of Existence (LoE), QAOA, Quantum Hamiltonian, Relational Physics, LLM Governance, Quantum AI, Emergent Cognition, Hybrid Intelligence.