22 problems

Let $M$ be a translation-invariant qubit three-dimensional TQFT stabilizer model. Two such models are equivalent under a locality-preserving unitary when a locality-preserving unit…

An invertible stabilizer code is an invertible lattice stabilizer phase, and a quantum cellular automaton (QCA) is considered modulo finite-depth quantum circuits and lattice trans…

Let $\mathbf{TS}^*$ be a proposed categorical spectrum of topological stabilizer codes, with $\mathbf{TS}^n$ its degree-$n$ component, and let $\mathbf Q^*(\mathrm{pt})$ denote the…

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…

Efficiency conjecture. Gibbs sampling is efficient at all temperatures for all classical and quantum stabilizer codes, except possibly around first-order phase transition points.

Coefficient-structure conjecture. There is some structure hidden in the coefficients of the high-order polynomial equation $f_{\mathcal{Q}}(t)$.

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

Let the code be the double-semion Pauli stabilizer code, a non-CSS code on ${\mathbb Z}_4$ qudits, mapped to a CSS code by doubling the number of qudits. Double-semion equivalence…

Consider generalized Pauli stabilizer models on nonprime-dimensional ${\mathbb Z}_d$ qudits. A condensation descendant of the ${\mathbb Z}_d$ toric code is a stabilizer model obtai…

A generalized Pauli stabilizer Hamiltonian is a Hamiltonian whose terms are commuting products of generalized Pauli operators on ${\mathbb Z}_d$ qudits. A two-dimensional translati…

Let $t$ be the number of correctable errors, and let $a_{0}$ be the parameter used in the shifted-bound construction. Define … where $n_{1},\dots,n_{a_{0}-1}$ are the intersection…

Let an $[[n,k,3]]$ stabilizer code be a quantum stabilizer code of length $n$, encoding $k$ qubits, and correcting one error. The parameters $n$ and $k$ denote the block length and…

Extremality conjecture. If a $[[n,0,d]]$ stabilizer code achieves the maximal concentratable entanglement on $n$ qubits, then it must be an extremal code.

A topological Pauli stabilizer code is a model whose ground-state subspace realizes topological order, and a finite-depth Clifford circuit with ancilla is a finite-depth quantum ci…

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…

The preceding question concerns whether one stabilizer code can be fault-tolerantly transformed into another, where fault-tolerant conversions respect the codes' notion of locality…

Let $R$ be a finite local commutative Frobenius ring with residue field, and let $C\subseteq R^{2n}$ be a free stabilizer code. Write $\overline{C}$ for the reduction of $C$ to the…

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.

Let a qubit stabilizer code implement logical gates by applying physical diagonal gates transversally. In the single- and two-qubit cases, such logical gates belong to the Clifford…

Let the quantum LDPC codes be constructed from the classical LDPC codes employed in the paper. A quantum error-correcting code is degenerate if a nontrivial Pauli operator of weigh…

Consider the model of two-dimensional STS Hamiltonians, whose logical operators can have pairs of zero-dimensional and two-dimensional geometric shapes, as in a classical ferromagn…

Let $H_A$ and $H_B$ be two-dimensional STS models. Denote their numbers of logical qubits by $k^{(A)}$ and $k^{(B)}$, and their numbers of zero-dimensional logical operators by…