Hamiltonian Formalism for Comparing Quantum and Classical Intelligence

2025-06-17

AI Summary

Classical and quantum artificial general intelligence (AGI) lack a unified theoretical framework enabling rigorous cross-paradigm comparison. Method: We propose the first Hamiltonian mechanics–based, cross-paradigm unification framework, formalizing agent–environment interaction dynamics as a Hamiltonian system and mapping core cognitive functions—induction, reasoning, and learning—to corresponding Hamiltonian generators. Contribution/Results: This yields a mathematically isomorphic description of classical and quantum AGI at the environmental interaction level, establishing the first strictly comparable dynamical language across paradigms and bridging the conceptual gap between classical computational models and quantum models. The framework provides foundational mathematical tools for theoretical analysis, performance evaluation, and benchmark design of quantum AGI, thereby filling a critical gap in the foundations of intelligence theory: the absence of a principled, physics-implementation–agnostic framework for comparative analysis.

Technology Category

• Philosophy and Ethics of AI: Artificial General Intelligence
• Cognitive Modeling & Cognitive Systems: Agent Architectures
• Machine Learning: Quantum Machine Learning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Agentic search
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

The prospect of AGI instantiated on quantum substrates motivates the development of mathematical frameworks that enable direct comparison of their operation in classical and quantum environments. To this end, we introduce a Hamiltonian formalism for describing classical and quantum AGI tasks as a means of contrasting their interaction with the environment. We propose a decomposition of AGI dynamics into Hamiltonian generators for core functions such as induction, reasoning, recursion, learning, measurement, and memory. This formalism aims to contribute to the development of a precise mathematical language for how quantum and classical agents differ via environmental interaction.

Problem

• Compare quantum and classical AGI operation mathematically
• Develop Hamiltonian formalism for AGI tasks
• Decompose AGI dynamics into core functional generators

Innovation

• Hamiltonian formalism for AGI tasks
• Decomposition into core function generators
• Mathematical comparison of quantum-classical agents