76 problems

Quantum Hamming bound conjecture. All quantum codes satisfy the quantum Hamming bound.

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

Polynomial-depth encoder conjecture. Any stabilizer QCC has a polynomial-depth encoder.

Hastings's conjecture. It is impossible to recover the quantum information with asymptotically vanishing error and probability greater than $1-t$.

Let $G$ and $H$ define a finite-support tiger code, and let the code's coherent-state logical constellations be the corresponding finite sets in phase space. Let the Euclidean dist…

Let $D$ denote the embedding dimension, and let a color route be the finite sequence of points in the qubit grid $[L]^{D-2}$ used to route a pair of qubits within the support of an…

Optimal constant-queue routing conjecture. The 3D Layer Code can be generalized using an optimal routing algorithm with $O(1)$ queue: all $X$ checks can be routed in parallel in on…

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 $(j_Z,j_X,k)$ 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 $[n,k,d]$ be a CSS code, and let a stabilizer check of weight $m\geq5$ be replaced by two checks through the bridged-star vertex-reduction construction, producing a new CSS cod…

Let a CSS code be represented by a chain complex, and suppose that the $X$- and $Z$-stabilizer sets have even sizes, so that stabilizers can be randomly paired and spliced independ…

Gauging-booster conjecture. The gauging booster will allow native logical action in arbitrary Clifford hierarchies implemented via twisted (gauged) 2D product codes, including HGP…

Simple $D$-join conjecture. There exists a minimum-size simple $D$-join.

Let $X$ be a $t$-dimensional cubical complex and let $\mathcal{F}$ be a sheaf satisfying the requirement in Dinur (2024). For integers $i,j,k,l$ satisfying … let…

Direct-product distillation conjecture. The state

Let $D(D_{4N})$ denote the stabilizer model based on the Drinfeld double of the dihedral group $D_{4N}$. When $4N=2^{n-1}$, realize the gates on a Hilbert space of $n$ physical qub…

Non-resonant CSS-code slowdown conjecture. Weighting the stabilizer terms by non-resonant coefficients should produce a similar slowdown of quantum dynamics in these models, potent…

Good-distance conjecture. The code described in this section nevertheless has good distance.

Let a Haar random code be the code obtained by applying an $n$-qubit Haar random unitary to a $k$-qubit input together with $n-k$ ancilla qubits initialized to $\ket{0^{n-k}}$. An…

Abstract-symmetry conjecture. The abstract symmetries of each torus $\varTheta$ can be used to implement logical Clifford gates for general LCA codes.

Maximum-length conjecture. Apart from some exceptions, the maximum length of an EAQMDS code over the relevant field is

IRUF distance-guarantee conjecture. Given the geometric similarity between toric codes and the other three code families, IRUF does not provide a distance guarantee for rotated tor…

Consider the constructed planar quantum low-density parity-check codes, which preserve geometric locality and the LDPC structure. Let the (pseudo)-threshold denote the noise thresh…

The code families are planar quantum low-density parity-check codes whose logical dimension is $k$ and whose code distance is $d$. Their stabilizers have a range determined by the…

Let a stabilizer-induced subgraph be a subgraph induced by a subset of stabilizer generators in the decoding graph, and let a trapping set (TS) be the relevant decoding-dynamical s…