Geometric Origin of Noise Bias and Parity Collapse in Quantized 11-Space (I11) as Underlying Structure of "Unfolded Distillation" in Biased Cat-Qubit Architectures
Boulfoul, Sebastian
Priority Note on Scale Invariant Deterministic Error Suppression Derived from the I11 Symmetry Logic Description: This priority note documents the first formulation of a deterministic mechanism for error suppression that arises directly from the internal symmetry of the quantized number space I11. The key insight is the introduction of the 1 divided by N normalization rule, which creates a half step reflection symmetry and divides all possible drift processes into two distinct parity sectors. This structure explains why phase preserving processes dominate while parity flipping processes are exponentially suppressed. The resulting error bias is not hardware dependent but follows from the intrinsic I11 geometry. This work establishes that the same symmetry logic underlying the I11 space also produces the specific form of biased noise and coherence enhancement observed in modern cat qubit architectures. The deterministic rotation angles and the stability ladder predicted by the I11 model match the operational structure used in contemporary folded and unfolded magic state distillation schemes, including those described in the 2025 Alice and Bob publication “Unfolded distillation: very low cost magic state preparation for biased noise qubits” (arXiv:2507.12511). The connection shows that the mechanism responsible for suppressing bit flip errors in biased noise systems had been formulated here earlier and independently, before its appearance in the recent literature. The present record establishes priority for the discovery of the underlying error suppression mechanism, the half step symmetry, the normalization rule 1 divided by N, and the resulting deterministic angle hierarchy that governs allowed operations in biased noise qubit systems. These concepts form the theoretical foundation for the error protection properties now observed experimentally. Type: Priority disclosure Version: Initial release Keywords: priority note, I11 number space, error suppression, biased noise, drift symmetry, parity structure, half step symmetry, normalization 1 divided by N, deterministic angles, coherence enhancement, cat qubits, magic state distillation, foundational discovery
•Nov 23, 2025•0 citations