Gauge-Theoretic Defect Representation of Quantum States: A Dimensional Threshold for Classical Simulatability

This paper introduces a geometric representation of quantum states using Z8 gauge theory with topological defects. Clifford gates correspond to gauge transformations; T‑gates correspond to inserting defects. In one dimension, expectation values of local observables are computed in O(n) time using an 8×8 transfer matrix. The accompanying code implements the 1D algorithm and confirms linear scaling. Higher‑dimensional theory is discussed in the paper but not implemented in the code.