Optical Geometric Multi-State Computing Units (O-GLUs): A New Computational Paradigm

摘要

We introduce Optical Geometric Logic Units (O-GLUs), a new computational paradigm that encodes information directly in the geometric degrees of freedom of light—phase (S¹), polarization (Poincaré sphere S²), and spatial modes—rather than binary states. Each O-GLU cell stores a point on a geometric manifold and partitions it into K logical regions, achieving an information density of log₂(K) bits per physical cell. O-GLUs offer three major advantages: (1) significantly higher information density than binary cells, (2) natural representation of angles, orientations, and periodic signals without quantization or conversion overhead, and (3) light-speed propagation and transformation. We present a complete mathematical framework for manifold-valued optical computation, analyze fundamental limits imposed by quantum shot noise and fabrication tolerances, and propose practical implementations using silicon photonics (ring resonators for phase, integrated polarization controllers, and hybrid multi-manifold designs). O-GLUs are positioned as specialized co-processors for geometry-intensive tasks in AI (e.g., pose estimation, geometric deep learning), robotics, RF beamforming, radar, and analog signal processing. This work establishes a third computational paradigm—geometric computing—that sits between classical digital and quantum systems, where the structure of computation mirrors the geometry of physical space.