The fibre-bundle conjecture for fault-tolerant logical gates

A fault-tolerant protocol consists of a quantum error-correcting code together with fault-tolerant gadgets implementing logical gates. Such a protocol is described by an appropriate fibre bundle equipped with a projective connection, whose parallel transport represents the induced logical operations.

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.

This conjecture is the paper's broad unifying claim that transversal-gate and topological fault tolerance admit a common geometric description. The supplied text does not establish its general validity or give evidence that it has been resolved.