AIMS Fractions as Quantum Rotation Angles: A Sexagesimal-Grounded Quantum-Compatible Architecture for Relational Intelligence Systems

Abstract

We present a formal mapping between the relational fractions of the Artificial Intelligence Modeling, Inference, and Management System (AIMS) — specifically the BPL (Bias Pressure Logic) coordinate values fi, wa, ai, and ea_abs — and the rotation gate set of universal quantum computation. We show that the four AIMS fractions, expressed in sexagesimal (base-60) angular coordinates as 15°, 30°, 45°, and 90°, correspond to the rotation operators R(π/6), R(π/4), R(π/3), and R(π/2) respectively — all members of the Clifford+T universal gate set. This mapping is not incidental: it reflects a deep structural alignment between the Plimpton 322 altitude-on-hypotenuse geometry that grounds the AIMS fractions and the Bloch sphere parameterization of qubit states. We further argue that the SMS/SML (Supervisory Management System / Supervisory Machine Language) component of AIMS, which requires simultaneous multi-scope, multi-state evaluation across 252 primitive-state-scope combinations, cannot achieve its full theoretical capacity in a classical computing environment and is naturally architected for quantum execution. The design principle we propose is: AIMS fractions specify quantum rotation angles, not quantum integers. This resolves encoding overhead problems associated with naive base-60 quantum implementations and aligns with the existing angular structure of AIMS. The paper addresses gaps in the current quantum-AI literature, particularly in: Nielsen & Chuang, "Quantum Computation and Quantum Information" (2000); Arute et al., "Quantum supremacy using a programmable superconducting processor" (2019); and Preskill, "Quantum Computing in the NISQ Era and Beyond" (2018).

Abstract of "AIMS Fractions as Quantum Rotation Angles: A Sexagesimal-Grounded Quantum-Compatible Architecture for Relational Intelligence Systems" by Cameron Brown, https://doi.org/10.5281/zenodo.19382847, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.