99 problems

Picard 2-group conjecture. It is conjectured that this algebraic structure captures part of the homotopy type of $\mathcal{M}(\mathcal{B})$.

A topological order is described through ground states of Hamiltonians with local interactions; the area law concerns the entanglement properties of such ground states, and project…

Let $S_{\rm topo}$ denote the topological entanglement entropy associated with a chosen partition or contour, and let TQO denote topological quantum order. Contour-independence con…

Consider the set of ground states constructed in the nearest-neighbor $S=1/2$ Klein model on the checkerboard lattice that satisfy the defining condition for topological quantum or…

Let $\Gamma$ range over allowed contours separating regions in a lattice system, and let $S_{\rm ent}$ be the entanglement entropy used to diagnose topological quantum order. Conto…

Let $\Gamma$ be a boundary surface of size $R$ separating two regions, and let $S_{\rm ent}$ denote their entanglement entropy. In $D=2$, suppose the entropy has the asymptotic are…

Finiteness conjecture for TQFTs. If the number of particle types is fixed, then there are only finitely many TQFTs.

Read–Rezayi conjecture. The Jones representation of the braid groups at an $r$-th root of unity describes the non-abelian statistics of fractional quantum Hall liquids at filling f…

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…

Let $A$ be an Abelian anyon theory, and let an Abelian topological code realize this theory on a torus. The code's logical dimension is the dimension of its encoded state space. Sq…

In the double Fibonacci model, let the encoded subspace be the span of the modular orbit states $\{M\ket{w}\}_M$, where $M$ ranges over modular matrices and … with $\omega^6=1$. A…

Let $\mathcal W$ denote the Witt group of $(2+1)$-dimensional topological quantum field theories, identified in the source with the Witt group of nondegenerate braided fusion categ…

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…

Non-Abelian p-loop condensation conjecture. Non-Abelian p-loop condensation serves as a general mechanism for transitions between fracton phases.

Pontryagin-dual anomaly classification conjecture. The classification is conjectured to be

Anomaly classification conjecture. The anomaly is classified by

Kitaev's monopole mass-gap conjecture. The monopoles have a mass gap, and the mass gap is extensive in the number of monopoles.

Let $G$ be a symmetry group. The Witt group of $G$-TQFTs is obtained from symmetry-enriched topological orders modulo the relation identifying phases that admit gapped symmetric in…

Perfectness conjecture. Every perfect theory of excitations can be realized by a quantum lattice model with a spatially local Hamiltonian.

Fibonacci–Ising stacking conjecture. The stacked model is part of a gapped phase in which properly infinite subsystems have type ${\mathrm{III}}_1$ algebras in ground-state sectors…

Gaiotto's conjecture. The boundary conformal field theory $\operatorname{BCFT}(\mathbf{F}_{\text{UV}\times \text{IR}})$ produces the information of the massless renormalization-gro…

Geometric-data conjecture. Within this construction, the intersection geometry is the only geometrical data needed to specify a unique fracton order.

$k$-planar X-cube conjecture. The resulting fracton order is $k$-planar, foliated, and $p$-modular, and depends only on $k$ and on the intersection properties of the chosen orienta…

Classification conjecture. With a suitable definition of enhanced $p$-theories and a better understanding of which $p$-theories are realizable, classifying $p$-modular fracton phas…

The $44$-dimensional $bZ_2^N$ homological code has logical gate … The construction is explicitly given for $N=2,3,4,5$. Extension conjecture. The same construction can be extended…