3 problems

Let $\mathcal{Q}_1$ and $\mathcal{Q}_2$ be subsystem stabilizer codes, and consider a fault-tolerant code-switching protocol between them. Let the set of transversal gates for each…

Linear-length measurement sequence conjecture. For any such family, there exists a fault-tolerant error-correction sequence consisting of $O(d)$ parity-check measurements.

Fibre-bundle conjecture. Fault-tolerant logical gates can always be expressed as arising from monodromies of an appropriate fibre bundle with a flat projective connection.