Hamiltonian Formalism for Comparing Quantum and Classical Intelligence
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.
Keywords
Cite
@article{arxiv.2506.14456,
title = {Hamiltonian Formalism for Comparing Quantum and Classical Intelligence},
author = {Elija Perrier},
journal= {arXiv preprint arXiv:2506.14456},
year = {2025}
}
Comments
This is the version accepted at AGI 25 (camera ready length limit of 10 pages plus references and appendices). Further work detailing bounds and limitations is in preparation. Comments and criticisms welcome