12 problems

Linear time-overhead conjecture. The time overhead can be reduced further with fault-tolerance sequences of length $O(d_D)$.

Let $C$ be a 3D Bacon-Shor code defined on a cubic lattice, with sheet-like stabilizer generators; its symmetric family on an $L\times L\times L$ lattice has parameters…

Let $C$ be a class of quantum codes called three-dimensional product codes, obtained from the corresponding three-dimensional product construction. A code is single shot when one n…

Let BB codes denote the Bivariate Bicycle codes considered with parameters $[[72,12,6]]$ under a circuit-level depolarizing noise model. Let $W$ be the decoding-window size, with t…

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…

The noise guessing decoding procedure is considered for quantum codes with code rate close to one, under noise statistics that are not approximately fixed and in applications requi…

In a deep neural network, consider the phenomenon that the network can exhibit natural fault tolerance without explicit intervention. Over-provisioning hypothesis. This phenomenon…

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

Weight nulling conjecture. For more complicated image-recognition tasks with large neural networks, such as VGG-16 networks, weight nulling could improve robustness by orders of ma…

Sufficiency conjecture. A protocol is fault-tolerant if there is a set of paths $mathring{\mathcal{F}}^{p}$ and a topological space $mathring{\mathcal{M}}$ such that the natural pr…

Main conjecture. For any such fault-tolerant unitary paths and loops, the natural proposals for pre-connections may be extended, after choosing an appropriate submanifold…

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.