In topological quantum computing, information is encoded in “knotted” quantum states of
topological phases of matter, thus being locked into topology to prevent decay. Topological …

A bstract This is the first part of a two-part work on a unified mathematical theory of gapped
and gapless edges of 2d topological orders. We analyze all the possible observables on the …

Topological order of a topological phase of matter in two spacial dimensions is encoded by
a unitary modular (tensor) category (UMC). A group symmetry of the topological phase …

This is the second part of a two-part work on the unified mathematical theory of gapped and
gapless edges of 2+ 1D topological orders. In Part I, we have developed the mathematical …

A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion
category E E. In this work, we propose that 2+ 1D topological/SPT orders with a fixed finite …

Quantum information processing has witnessed significant advancements through the
application of qubit-based techniques within universal gate sets. Recently, exploration …

We describe several methods of constructing R-matrices that are dependent upon many
parameters, for example unitary R-matrices and R-matrices whose entries are functions. As …

Bicommutant categories are higher categorical analogs of von Neumann algebras that were
recently introduced by the first author. In this article, we prove that every unitary fusion …

A bstract We study Galois actions on 2+ 1D topological quantum field theories (TQFTs),
characterizing their interplay with theory factorization, gauging, the structure of gapped …

We study novel invariants of modular categories that are beyond the modular data, with an
eye towards a simple set of complete invariants for modular categories. Our focus is on the …