Extend exact logical-error analysis to escape and grafting stages

Extend the exact logical-error-rate analysis of magic state cultivation to include the escape and grafting stages beyond the injection, double-checking, code-growth, and noiseless-readout components analyzed for the distance- and distance- circuits.

Background

The paper develops an exact Pauli-propagation and tensor-contraction method for calculating acceptance probabilities and post-selected logical error rates in the cultivation circuits used for distance and distance magic-state preparation. Its circuit analysis explicitly excludes the escape, grafting, and decoding stages, so the reported exact rates apply only to the analyzed cultivation portions.

The authors identify extending the calculation to the escape and grafting stages as unresolved future work. Completing this extension would enable exact or systematically controlled logical-error estimates for a more complete magic-state cultivation pipeline rather than only for the cultivation subcircuits studied here.