Related papers: Pauli stabilizer models of twisted quantum doubles
Braiding and fusion rules of topological excitations are indispensable topological invariants in topological quantum computation and topological orders. While excitations in 2D are always particle-like anyons, those in 3D incorporate not…
It is well known that the abelian $Z_2$ anyonic model (toric code) can be realized on a highly entangled two-dimensional spin lattice, where the anyons are quasiparticles located at the endpoints of string-like concatenations of Pauli…
We study measurement-induced symmetry-protected topological (SPT) order in a wide class of quantum random circuit models by combining calculations within the stabilizer formalism with tensor network simulations. We construct a family of…
A model for studying atomtronic devices and circuits based on finite temperature Bose-condensed gases is presented. The approach involves numerically solving equations of motion for atomic populations and coherences, derived using the…
We study two-dimensional translation-invariant CSS stabilizer codes over prime-dimensional qudits on the square lattice under twisted boundary conditions, generalizing the Kitaev $\mathbb{Z}_p$ toric code by augmenting each stabilizer with…
Despite the exponential overhead to describe general multi-qubit quantum states and processes, efficient methods for certain state families and operations have been developed and utilised. The stabilizer formalism and the Gottesman-Knill…
We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a…
A variety of local index formulas is constructed for quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as…
The vortex-boson (or Abelian-Higgs, XY) duality in 2+1 dimensions demonstrates that the quantum disordered superfluid is equivalent to an ordered superconductor and the other way around. Such a duality structure should be ubiquitous but in…
We study the twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories on $S^1 \times \Sigma$ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum…
We consider the double scaling limit of a model of Pauli spin operators recently studied in Hanada et al. [1] and evaluate the moments of the Hamiltonian by the chord diagrams. We find that they coincide with those of the double scaled SYK…
We investigate a square-lattice architecture of superconducting transmon qubits with inter-qubit interactions mediated by inductive couplers. Therein, the inductive couling between the qubit and couplers is suggested to be designed into the…
The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
The recent discovery of higher-order topological insulators (TIs) has opened new possibilities in the search for novel topological materials and metamaterials. Second-order TIs have been implemented in two-dimensional (2D) systems…
We propose a new discrete model---the twisted quantum double model---of 2D topological phases based on a finite group $G$ and a 3-cocycle $\alpha$ over $G$. The detailed properties of the ground states are studied, and we find that the…
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization…
Hopfions are a class of three-dimensional (3D) solitons which are built as vortex tori carrying intrinsic twist of the toroidal core. They are characterized by two independent topological charges, \textit{viz}., vorticity $S$ and winding…
We present a general approach to the bulk-boundary correspondence of noninvertible topological phases, including both topological and fracton orders. This is achieved by a novel bulk construction protocol where solvable $(d+1)$-dimensional…
The Turaev-Viro invariant for a closed 3-manifold is defined as the contraction of a certain tensor network. The tensors correspond to tetrahedra in a triangulation of the manifold, with values determined by a fixed spherical category. For…