18 problems

Let $W_2$ denote the two-anyon-pair state, and let $\Sigma_2$ be a genus-$2$ handlebody. The Clifford group orbit of $W_2$ is represented by removing two solid tori from the interi…

Chargeon–kelvon correspondence conjecture. The chargeon part of a dyon corresponds to the spin mode of the kelvon attached to the vortex.

Efficient universality conjecture. Based on experimental evidence, the four operators above are efficiently universal.

Optimal efficiency conjecture. The non-semisimple model associated with the generic part of the category of unrolled $cmathfrak{sl}_2$ at a fourth root of unity achieves an optimal…

Multi-qubit double-braiding universality conjecture. The universality of double-braidings should also hold for the multi-qubit case, that is, for spaces of more than three anyons.

Property F conjecture. An anyon $X$ is braiding universal if and only if

The reductions in Theorems 1 and 2 produce diagrams with distinct properties. Combined reduction conjecture. There exists a single reduction that builds a knot $K'$ with a combinat…

Property F conjecture. The category $\mcC$ has property F if, and only if,

Let $R$ be a unitary $R$-matrix, meaning a nonsingular matrix satisfying the quantum Yang–Baxter equation and whose dimension is a square. Finite representation conjecture. A singl…

Quantum-dimension criterion. The anyon $a$ is braiding universal if and only if $\dim(a)^2$ is not an integer.

Let $V^{1111}_0$ denote the qubit model shown in the paper's Figure 1, and allow measurements of total charges of metaplectic anyons. A model is Ising like if its braidings and the…

Let $p$ be an odd prime with $p\geq 5$, and consider the metaplectic anyon system $SO(p)_2$. A universal anyonic computing model is a model in which anyons, braidings, and the rele…

Let $\mathcal{C}$ be a modular category, and let $D^2$ denote its global dimension. For each mapping class group associated with a surface, the modular category determines a repres…

A Property F TQFT is a topological quantum field theory whose associated braid group representations have finite image. A topological quantum computing model is efficiently simulab…

An explicit local unitary TQFT is a unitary TQFT whose associated braid group representations admit the refined locality described in the paper. A braid representation is braiding-…

Topological quantum computation uses representations of braid groups to describe the actions of quantum bits (qubits). Topological fault-tolerance conjecture. The construction shou…

Topological qubit liquid conjecture. Every doubled MTC can be realized as a topological qubit liquid, and the groundstates

Finiteness and universality conjecture. There are only finitely many equivalence classes of MTCs of any fixed rank, and a unitary modular tensor category is universal for anyonic q…