14 problems

Given a quantum error-correcting code encoding $k$ logical qubits, characterize the codes and fusion strategies for which the induced logical fusion succeeds for every pattern in w…

An impure $[[n,k,3]]$ stabilizer code is a quantum stabilizer code encoding $k$ logical qubits into $n$ physical qubits, with minimum distance $3$ and with nontrivial stabilizer el…

Good GKP codes conjecture. The code is likely to be good, encodes $k=n$ qubits, and has distance

Let $(j_Z,j_X,k)$ be any balanced triple satisfying … The corresponding HA-side and MN-side classical constituent codes are the codes associated with this triple, and a balanced tr…

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…

Let $D=\operatorname{diag}(d_1,\ldots,d_n)$ be a type, and let $\mathcal{L}\subseteq\mathcal{L}^{\perp}\subseteq\mathbb{R}^{2n}$ be a symplectically integral lattice of type $D$. H…

Transversal Clifford impossibility conjecture. There exists no stabilizer code where transversal Clifford gates realize the logical C-QSK circuit for any non-trivial exponentiated…

Rotor-code conjecture. Under these assumptions, $\phi_\infty(\mathcal{S})$ represents a good quantum LDPC rotor code.

An $\left[\!\left[n,k\!:\!m,d\!:\!c\right]\!\right]_{q}$ hybrid stabilizer code has length $n$, quantum dimension $k$, classical dimension $m$, quantum minimum distance $d$, and cl…

A lax-topological $D$-dimensional Hamiltonian schema satisfies $TQO0$, $TQO1$, and $TQO2$, and there exist constants $\alpha$ and $\beta$ depending only on $D$ such that … for ever…

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

Let $d$ be the distance parameter, let $n$ denote the block length, and let unrestricted DS codes be quantum data-syndrome codes without a non-degeneracy restriction. Write the Ham…

Asymptotic Hamming-bound conjecture. For any $d$ there exists $n(d)$ such that for $n\geq n(d)$ the Hamming bound in equation (HBnondeg) holds for unrestricted data-syndrome codes.

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.