We investigate topological order on fractal geometries embedded in $n$ dimensions. In particular, we diagnose the existence of the topological order through the lens of quantum information and geometry, i.e., via its equivalence to a quantum error-correcting code with a macroscopic code distance or the presence of macroscopic systoles in systolic geometry. We first prove a no-go theorem that $\mathbb{Z}_N$ topological order cannot survive on any fractal embedded in 2D. For fractal lattice models embedded in 3D or higher spatial dimensions, $\mathbb{Z}_N$ topological order survives if the boundaries of the interior holes condense only loop or membrane excitations. Moreover, for a class of models containing only loop or membrane excitations, ...
Topological quantum error-correcting codes are a family of stabilizer codes that are built using a l...
In this work, we develop a coupled layer construction of fracton topological orders in d=3 spatial d...
We consider the problem of converting a product state to a ground state of a topologically ordered s...
Recently, a class of fractal surface codes (FSCs), has been constructed on fractal lattices with Hau...
We show that interactions can drive a class of higher order topological superconductors (HOTSCs) int...
We study how graph states on fractal lattices can be used to perform measurement-based quantum compu...
We present a large class of three-dimensional spin models that possess topological order with stabil...
Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two su...
Three-dimensional topological insulators support gapless Dirac fermion surface states whose rich top...
In this paper, we study the holographic quantum error correcting code properties in different bounda...
Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superco...
We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), ca...
In this article we extend on work which establishes an analology between one-way quantum computation...
Higher-order topological insulators, which support lower-dimensional topological boundary states tha...
The exploration of topologically-ordered states of matter is a long-standing goal at the interface o...
Topological quantum error-correcting codes are a family of stabilizer codes that are built using a l...
In this work, we develop a coupled layer construction of fracton topological orders in d=3 spatial d...
We consider the problem of converting a product state to a ground state of a topologically ordered s...
Recently, a class of fractal surface codes (FSCs), has been constructed on fractal lattices with Hau...
We show that interactions can drive a class of higher order topological superconductors (HOTSCs) int...
We study how graph states on fractal lattices can be used to perform measurement-based quantum compu...
We present a large class of three-dimensional spin models that possess topological order with stabil...
Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two su...
Three-dimensional topological insulators support gapless Dirac fermion surface states whose rich top...
In this paper, we study the holographic quantum error correcting code properties in different bounda...
Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superco...
We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), ca...
In this article we extend on work which establishes an analology between one-way quantum computation...
Higher-order topological insulators, which support lower-dimensional topological boundary states tha...
The exploration of topologically-ordered states of matter is a long-standing goal at the interface o...
Topological quantum error-correcting codes are a family of stabilizer codes that are built using a l...
In this work, we develop a coupled layer construction of fracton topological orders in d=3 spatial d...
We consider the problem of converting a product state to a ground state of a topologically ordered s...