Related papers: Magic Boundaries of 3D Color Codes
We introduce boundary special generic maps, a class of submersions from manifolds with boundary to Euclidean spaces whose restriction to the boundary has only boundary definite fold points as its singular points. We derive the…
This paper presents three main results on coloring discrete $d$-pseudomanifolds: $(1)$ the general chromatic bounds $d+1 \leq X(K) \leq 2d+2$ for any $d$-pseudomanifold $K$; $(2)$ an improved bound $X(K) \leq 2d+1$ for pseudomanifolds…
2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics…
We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is neither scale-invariant nor smooth, the usual methodology to obtain limit laws…
We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different…
Twists are defects that are used to encode and process quantum information in topological codes like surface and color codes. Color codes can host three basic types of twists viz., charge-permuting, color-permuting and domino twists. In…
Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study…
The present paper mainly studies limits and constructions of insertion and deletion (insdel for short) codes. The paper can be divided into two parts. The first part focuses on various bounds, while the second part concentrates on…
Intersecting codes are linear codes where every two nonzero codewords have non-trivially intersecting support. In this article we expand on the theory of this family of codes, by showing that nondegenerate intersecting codes correspond to…
We present CT-Bound, a robust and fast boundary detection method for very noisy images using a hybrid Convolution and Transformer neural network. The proposed architecture decomposes boundary estimation into two tasks: local detection and…
Investigating the sound field in and around ducts is an important topic in acoustics, e.g. when simulating musical instruments or the human vocal tract. In this paper a method that is based on the boundary element method in 3D combined with…
We consider non-binary product codes with MDS components and their iterative row-column algebraic decoding on the erasure channel. Both independent and block erasures are considered in this paper. A compact graph representation is…
Bulk-boundary correspondence is a concept for topological insulators and superconductors that determines the existence of topological boundary states within the tenfold classification table. Contrary to this belief, we demonstrate that…
Let $X$ be a proper geodesic metric space. We give a new construction of the Morse Boundary that realizes its points as equivalence classes of functions on $X$ which behave similar to the "distance to a point" function. When $G=\langle S…
We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show…
In a recent work, Bombin, Duclos-Cianci, and Poulin showed that every local translationally invariant 2D topological stabilizer code is locally equivalent to a finite number of copies of Kitaev's toric code. For 2D color codes, Delfosse…
A model of bound state formation from the delocalized edge states of 2D topological insulator is derived by considering the effects of magnetic barriers attached to the edge of the HgTe/CdTe quantum well. The resulting structure has a…
Let $D$ be a straight-line drawing of a graph. The rectilinear 2-colored crossing number of $D$ is the minimum number of crossings between edges of the same color, taken over all possible 2-colorings of the edges of $D$. First, we show…
The boundary of symmetry-protected topological states (SPTs) can harbor new quantum anomaly phenomena. In this work, we characterize the bosonic anomalies introduced by the 1+1D non-onsite-symmetric gapless edge modes of 2+1D bulk bosonic…
Color codes are a class of topological quantum codes with a high error threshold and large set of transversal encoded gates, and are thus suitable for fault tolerant quantum computation in two-dimensional architectures. Recently,…