The Law of Coherence and the Foundations of Coherent Computing

Coherence across many-body degrees of freedom is governed by a simple empirical law. Defining a global order parameter C from phase samples, we observe three robust behaviors: (1) Gaussian dephasing, where C(σ) behaves approximately like exp(−ασ²); (2) return-to-attractor dynamics, where C relaxes back toward a fixed point C* with rate κ; and (3) finite-size scaling, where C(N) behaves approximately like C₀ − β/N and converges toward a stable limit C* ≈ 1. These relations appear consistently across simulations and hardware-stress surrogates over wide sweeps of disorder and system size. Together, they define a minimal phenomenological framework for “coherent computing,” where architectures are judged by how they shape, rather than suppress, phase noise.