The Quantum Learning Flow: A Unified Algorithm for Physics

The Central Identity: From Three Domains to One

The Quantum Learning Flow (QLF) is a single mathematical rule that unifies three seemingly different fields. Quantum dynamics, information geometry, and machine learning are all shown to be different expressions of the same fundamental process. This identity is not just a metaphor but a rigorous mathematical equivalence. It means that the way a quantum system evolves towards its ground state is identical to the way an optimal learning algorithm updates its beliefs, and both are equivalent to the natural path on a statistical manifold.

This identity has profound implications. It suggests that the fundamental laws of physics, like the Schrödinger equation, are not fundamental at all. They are emergent properties of an information-theoretic process. Quantum mechanics can be seen as a special case of a very general and efficient learning process. This perspective turns the traditional view on its head: instead of starting with quantum postulates, we start with a simple, deterministic rule (the QLF) and derive quantum mechanics as a consequence.

• Normalized Imaginary-Time Propagation (NITP) from quantum mechanics
• Fisher-Rao natural gradient flow (FR-Grad) from information geometry
• Mirror descent with KL-divergence (MD-KL) from machine learning

The Rosetta Stone: A Dictionary for Physics

The table below summarizes how concepts from each domain correspond. In quantum physics, the state is a wavefunction. In information geometry, the state is a probability distribution. In machine learning, the state is a probability vector. Each has its own version of an “energy” or “loss” function. The QLF shows that the evolution in all three cases is identical. This means that theorems from one field, like the convergence of mirror descent, can directly translate to properties in another, like the stability of matter in quantum mechanics.

This unified view suggests that space, time, and matter might all be emergent properties of an underlying computational process. The universe is not just described by mathematics; in a very real sense, it may be mathematics, or more precisely, it may be a computation. The implications for problems like the firewall paradox and the nature of quantization are profound and are explored in the subsequent sections.