Quantum particles and AI decision-making algorithms have been found to be governed by the exact same mathematical laws.
March 31, 2026
Original Paper
The Triality of Radial Nonlinear Dynamics: Analysis of Riccati, Schrödinger, and Hamilton--Jacobi--Bellman Equations
arXiv · 2603.27772
The Takeaway
Researchers proved a 'triality' connecting quantum mechanics, growth equations, and optimal control (the math behind AI planning). This means that a quantum particle moving through a potential field is mathematically identical to an AI agent calculating the most efficient route to a goal.
From the abstract
This study establishes a comprehensive mathematical framework for the analysis of radial differential equations, identifying a fundamental connection between three distinct classes of problems: the nonlinear Riccati equation, the linear Schrödinger equation, and the Hamilton--Jacobi--Bellman equation for stochastic control. We prove the existence and uniqueness of regular solutions on both bounded and unbounded domains, identifying sharp growth rates and asymptotic behaviors. Furthermore, we con