We consider Kitaev's quantum double model based on a finite group $ G $ and describe
quantum circuits for (a) preparation of the ground state,(b) creation of anyon pairs separated …

Motivated by quantum simulation, we consider lattice Hamiltonians for Yang-Mills gauge
theories with finite gauge group, for example a finite subgroup of a compact Lie group. We …

Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum
many-body physics. We develop a general approach to constructing gauge-invariant or …

We study the stability with respect to a broad class of perturbations of gapped ground-state
phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of …

The recent article by Jones et al.[arXiv: 2307.12552 (2023)] gave local topological order
(LTO) axioms for a quantum spin system, showed they held in Kitaev's Toric Code and in …

Realizing topological orders and topological quantum computation is a central task of
modern physics. An important but notoriously hard question in this endeavor is how to …

We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with
underlying quantum double D (G) symmetry, where G is a finite group. We provide projection …

We introduce a set of axioms for locally topologically ordered quantum spin systems in terms
of nets of local ground state projections, and we show they are satisfied by Kitaev's Toric …

Non-Abelian defects that bind Majorana or parafermion zero modes are prominent in
several topological quantum computation schemes. Underpinning their established …

We show that in renormalization group (RG) flow the low-energy states form a code
subspace that is approximately protected against the local short-distance errors. To …