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Holonomy Obstructions to Composability in Fault-Tolerant Quantum Circuits

L. D. L. Nguyen

Published Feb 13, 2026• 0 citations
Publisher

Abstract

This paper develops a realization-level geometric framework for sequential quantum evolution and identifies a structural distinction between local reduced-channel correctness and coherent global composability in fault-tolerant quantum computation. Threshold theorems certify each extended rectangle (ExRec) through reduced logical channels generated by Stinespring dilations, but the underlying realization-level transport is not uniquely determined by the reduced channel itself. We show that distinct realization-equivalent dilations can accumulate higher-order commutator structure under coherent sequential composition, producing logical drift invisible to isolated local certification. Using BCH and Magnus transport theory, we prove that there exist finite-dimensional realization architectures with arbitrarily accurate local ε-correct ExRecs whose ordered realization transport develops order-one logical deviation after sufficiently long sequential depth. The obstruction is governed by a projected logical curvature operator measuring whether realization-level commutator geometry survives projection onto the logical subsystem. We formulate the resulting structure geometrically through ordered non-autonomous transport on a Stinespring dilation bundle equipped with logical connection and holonomy structure, placing fault-tolerant quantum evolution within a unified realization-level transport geometry.

DOI
10.5281/zenodo.18632979

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