Data for "Separating Geometry From Interference in Constrained Quantum Optimization"

This repository contains the numerical data, and analysis scripts supporting the manuscript “Separating Geometry From Interference in Constrained Quantum Optimization.” The manuscript develops a framework that separates three components of constrained quantum optimization algorithms: mixer-induced transport geometry on an encoded product space; coherent interference among transported amplitudes; problem-dependent classical maps applied to measured samples. For complete-graph block-(XY) mixers acting on one-hot product spaces, the code implements the exact shell-transfer coefficients, the finite radial recursion, and the normalized stochastic shell kernel derived in the manuscript. It also contains numerical diagnostics comparing different (XY)-mixer geometries and evaluates the preservation of shell-resolved transport under product-formula implementations of the complete-graph mixer. The archived material supports the following results and figures: evaluation of the one-block complete-graph (XY)-mixer amplitudes; construction of the shell-transfer coefficients (T_{r,t}(\beta)); iteration of the exact radial path-mass recursion; construction of the normalized radial Markov kernel; evaluation of radial drift, variance, and stationary shell distributions; comparison of complete, cycle, path, star, and sparse (XY)-mixer geometries; calculation of one-site absolute transfer factors; calculation of Hamming-shell and geometry-refined lumpability defects; generation of shell-sampling profiles; simulation of Trotterized complete-graph (XY) mixers; calculation of local quotient defects and shell-kernel errors; evaluation of certified Trotter step counts and logical exchange depths; generation of the numerical data used in the manuscript figures and tables. The repository is intended to make the numerical results reproducible and to provide a reusable implementation of the shell-transport formalism for constrained quantum optimization on product spaces. The manuscript should be cited together with this archive when the code or data are used.