Minimum Weight Perfect Matching Decoder for a Non-Orientable Stabilizer Code: Antipodal Shortcut and Hardware Validation

We present the first minimum weight perfect matching (MWPM) decoder designed for a non-orientable stabilizer code: the Klein bottle quantum error-correcting code. The decoder incorporates an antipodal shortcut: in the Klein bottle code, the non-orientable boundary identification connects two syndrome qubits via a single edge, giving them defect-graph distance 1 rather than the toric Manhattan distance of 4. A standard toric MWPM decoder fails on 25% of single-qubit errors (the four vertical edges on the non-orientable boundary); the Klein decoder corrects all 64 single-qubit errors across all four logical sectors analytically. Hardware validation on IBM Fez (Heron r2, 156 qubits) confirms 6/6 correction scenarios at Z = 688–730σ, including both antipodal-edge scenarios. Multi-session reproducibility across six calibration sessions and double-error logical fidelity (98.57% single-error, one identified degenerate pair at f = 0.51%) are reported in the appendix. This is the fifth paper in a series on the experimental characterisation of the Klein bottle stabilizer code on superconducting quantum hardware. Companion papers: Paper 1: Code existence, GSD=4, kill test Z=691σ https://doi.org/10.5281/zenodo.19284050 Paper 2: δ-family, topological parameter encoding https://doi.org/10.5281/zenodo.19286677 Paper 3: Non-orientable logical algebra, holonomy https://doi.org/10.5281/zenodo.19287977 Paper 4: Six Simultaneous Non-Orientable Stabilizer Codes https://doi.org/10.5281/zenodo.19333513