Experimental Realization of the Klein Bottle Stabilizer Code on a Superconducting Processor

Comprehensive experimental account of non-orientable stabilizer codes on superconducting quantum hardware. This work consolidates and extends a five-paper series on the Klein bottle stabilizer code, and reports the first experimental realisation of the real projective plane (RP²) stabilizer code. Key results: Klein bottle code confirmed at distances d=2, 3, 4 with a working MWPM decoder (antipodal shortcut, 6/6 hardware validation at Z=688–730σ) ; transversal Clifford group with O (1) gate overhead; 12 logical qubits on 156 physical qubits at CV=0. 01; δ-family confirmed at d=2, 3, 4. RP² 4×4 code: both boundary twists confirmed simultaneously (266–571σ, zero noise bits in dominant), logical qubit verified with ZL contrast 0. 885, GSD=2 confirmed. Transversal T^⊗32 ruled out analytically; code deformation identified as the open problem. Raw syndrome count data for all experiments available at https: //github. com/theoricline/klein-bottle-qec/data 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 Paper 5: MWPM Decoder for a Non-Orientable Stabilizer Code https: //doi. org/10. 5281/zenodo. 19451825