Related papers: Visualising Quantum Product Codes
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
Publicly available collections of drug-like molecules have grown to comprise 10s of billions of possibilities in recent history due to advances in chemical synthesis. Traditional methods for identifying "hit" molecules from a large…
Computer graphics seeks to deliver compelling images, generated within a computing budget, targeted at a specific display device, and ultimately viewed by an individual user. The foveated nature of human vision offers an opportunity to…
The 'boxicity' ('cubicity') of a graph G is the minimum natural number k such that G can be represented as an intersection graph of axis-parallel rectangular boxes (axis-parallel unit cubes) in $R^k$. In this article, we give estimates on…
A unique decoding algorithm for general AG codes, namely multipoint evaluation codes on algebraic curves, is presented. It is a natural generalization of the previous decoding algorithm which was only for one-point AG codes. As such, it…
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…
Generalized bicycle (GB) codes have emerged as a promising class of quantum error-correcting codes with practical decoding capabilities. While numerous asymptotically good quantum codes and quantum low-density parity-check code…
It is fundamental for science and technology to be able to predict chemical reactions and their properties. To achieve such skills, it is important to develop good representations of chemical reactions, or good deep learning architectures…
We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the…
Automated visualization design navigates a tension between symbolic systems and generative models. Constraint solvers enforce structural and perceptual validity, but the rules they require are difficult to author and too rigid to capture…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
Although product graphs (PGs) have gained increasing attentions in recent years for their successful applications in product search and recommendations, the extensive power of PGs can be limited by the inevitable involvement of various…
We present a simple linear programming (LP) based method to learn compact and interpretable sets of rules encoding the facts in a knowledge graph (KG) and use these rules to solve the KG completion problem. Our LP model chooses a set of…
Ontology-based knowledge graph (KG) construction is a core technology that enables multidimensional understanding and advanced reasoning over domain knowledge. Industrial standards, in particular, contain extensive technical information and…
Quantum error correction (QEC) is a crucial prerequisite for future large-scale quantum computation. Finding and analyzing new QEC codes, along with efficient decoding and fault-tolerance protocols, is central to this effort. Holographic…
Current distributed data fabrics lack a rigorous mathematical foundation, often relying on ad-hoc architectures that struggle with consistency, lineage, and scale. We propose a mathematical framework for data fabrics, unifying heterogeneous…
The traceability of granite blocks consists in identifying each block with a finite number of color bands which represent a numerical code. This code has to be read several times throughout the manufacturing process, but its accuracy is…
Higher-dimensional spaces are ubiquitous in applications of mathematics. Yet, as we live in a three-dimensional space, visualizing, say, a four-dimensional space is challenging. We introduce a novel method of interactive visualization of…
Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for constructing quantum error-correcting codes with desirable…
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…