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The folding of monolayer graphene leads to new layered systems, termed twisted bilayer graphene (TBG), generally displaying a certain interlayer rotation away from crystallographic alignment. We here present an atomic force microscopy study…
We present a simple mechanism, which can be randomised, for constructing sparse $3$-uniform hypergraphs with strong expansion properties. These hypergraphs are constructed using Cayley graphs over $\mathbb{Z}_2^t$ and have vertex degree…
Topological subsystem codes were proposed by Bombin based on 3-face-colorable cubic graphs. Suchara, Bravyi and Terhal generalized this construction and proposed a method to construct topological subsystem codes using 3-valent hypergraphs…
A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By…
Present-day communication systems routinely use codes that approach the channel capacity when coupled with a computationally efficient decoder. However, the decoder is typically designed for the Gaussian noise channel and is known to be…
Codes on hypergraphs are an extension of the well-studied family of codes on bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes on regular t-partite hypergraphs whose minimum distance improves earlier estimates…
Hypergraph expanders are hypergraphs with surprising, non-intuitive expansion properties. In a recent paper, the first author gave a simple construction, which can be randomized, of $3$-uniform hypergraph expanders with polylogarithmic…
In this paper, we study a class of spatially coupled turbo codes, namely partially information- and partially parity-coupled turbo codes. This class of codes enjoy several advantages such as flexible code rate adjustment by varying the…
Let G be a simple, connected graph on n vertices. Let d_G(u,v) denote the distance between vertices u and v in G. A subgraph H of G is isometric if d_H(u,v)=d_G(u,v) for every u,v in V(H). We say that G is a distance-preserving graph if G…
Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…
To meet the evolving data rate requirements of emerging wireless communication technologies, many parallel architectures have been proposed to implement high throughput turbo decoders. However, concurrent memory reading/writing in parallel…
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. The problem of finding edge-disjoint Hamiltonian cycles in a given regular graph has many applications in combinatorial optimization and…
We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…
We give formulas, in terms of graph theoretical invariants, for the minimum distance and the generalized Hamming weights of the linear code generated by the rows of the incidence matrix of a signed graph over a finite field, and for those…
The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the…
In this paper, we consider the unit graph $G(\mathbb{Z}_{n})$, where $n=p_{1}^{n_{1}} \text{ or } p_{1}^{n_{1}}p_{2}^{n_{2}} \text{ or } p_{1}^{n_{1}}p_{2}^{n_{2}}p_{3}^{n_{3}}$ and $p_{1}, p_{2}, p_{3}$ are distinct primes. For any prime…
Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…
We describe an approach to bounded-memory computation of persistent homology and betti barcodes, in which a computational state is maintained with updates introducing new edges to the underlying neighbourhood graph and percolating the…
A computationally efficient workflow for obtaining the low-energy symmetric tight-binding Hamiltonians for twisted multilayer systems is presented in this work. We apply this scheme to twisted bilayer graphene at the first magic angle. As…