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This is a PhD Thesis on the connection between subfactors (more precisely, their corresponding fusion categories) and Conformal Field Theory (CFT). Besides being a mathematically interesting topic on its own, subfactors have also attracted…
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
The degree of entanglement of random pure states in bipartite quantum systems can be estimated from the distribution of the extreme Schmidt eigenvalues. For a bipartition of size M\geq N, these are distributed according to a…
By interpreting the fusion matrix as an adjacency matrix we associate a loop model to every primary operator of a generic conformal field theory. The weight of these loop models is given by the quantum dimension of the corresponding primary…
A common problem in data analysis is the separation of signal and background. We revisit and generalise the so-called $sWeights$ method, which allows one to calculate an empirical estimate of the signal density of a control variable using a…
Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…
Under unitary evolution, a typical macroscopic quantum system is thought to develop wavefunction branches: a time-dependent decomposition into orthogonal components that (1) form a tree structure forward in time, (2) are approximate…
Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be…
Cluster-Weighted Modeling (CWM) is a flexible mixture approach for modeling the joint probability of data coming from a heterogeneous population as a weighted sum of the products of marginal distributions and conditional distributions. In…
We introduce canonical weight normalization for convolutional neural networks. Inspired by the canonical tensor decomposition, we express the weight tensors in so-called canonical networks as scaled sums of outer vector products. In…
We examine the use of weight enumerators for analyzing tensor network constructions, and specifically the quantum lego framework recently introduced. We extend the notion of quantum weight enumerators to so-called tensor enumerators, and…
The problem "Given a Boolean function $f$ of $n$ variables by its truth table vector. Find (if exists) a vector $\alpha \in \{0,1\}^n$ of maximal (or minimal) weight, such that $f(\alpha)= 1$." is considered here. It is closely related to…
The determination of weight distribution of cyclic codes involves evaluation of Gauss sums and exponential sums. Despite of some cases where a neat expression is available, the computation is generally rather complicated. In this note, we…
Recently, Graph Convolutional Networks (GCNs) have proven to be a powerful mean for Computer Aided Diagnosis (CADx). This approach requires building a population graph to aggregate structural information, where the graph adjacency matrix…
We develop a new method for representing Hilbert series based on the highest weight Dynkin labels of their underlying symmetry groups. The method draws on plethystic functions and character generating functions along with Weyl integration.…
Convolutional Neural Networks (CNNs) are known for requiring extensive computational resources, and quantization is among the best and most common methods for compressing them. While aggressive quantization (i.e., less than 4-bits) performs…
In recent years, quantum machine learning has seen a substantial increase in the use of variational quantum circuits (VQCs). VQCs are inspired by artificial neural networks, which achieve extraordinary performance in a wide range of AI…
Quantum error-correction codes (QECCs) are a vital ingredient of quantum computation and communication systems. In that context it is highly desirable to design QECCs that can be represented by graphical models which possess a structure…
A generator matrix of a linear code $\C$ over $\gf(q)$ is also a matrix of the same rank $k$ over any extension field $\gf(q^\ell)$ and generates a linear code of the same length, same dimension and same minimum distance over $\gf(q^\ell)$,…