Related papers: Construction of quantum codes based on self-dual o…
We study a set of scattering matrices of quantum graphs containing minimal number of passbands, i.e., maximal number of zero elements. The cases of even and odd vertex degree are considered. Using a solution of inverse scattering problem,…
Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation…
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…
We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear…
We study triangle decompositions of graphs. We consider constructions of classes of graphs where every edge lies on a triangle and the addition of the minimum number of multiple edges between already adjacent vertices results in a strongly…
We discuss the construction of $n$-qubit pure states with maximum bipartite entanglement across all possible choices of $k$ vs $n-k$ bi-partitioning, which implies that the Von Neumann entropy of every $k$-qubit reduced density matrix…
Local unitary invariance and the notion of negativity fonts are used as the principle tools to construct four qubit invariants of degree 8, 12, and 24. A degree 8 polynomial invariant that is non-zero on pure four qubit states with…
In this paper, we present two new ways of quantum synchronization coding based on the $(\bm{u}+\bm{v}|\bm{u}-\bm{v})$ construction and the product construction respectively, and greatly enrich the varieties of available quantum…
New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of…
Hybrid codes simultaneously encode both quantum and classical information into physical qubits. We give several general results about hybrid codes, most notably that the quantum codes comprising a genuine hybrid code must be impure and that…
Let $\mathbb{F}_q$ be a finite field with $q=p^{e}$ elements, where $p$ is a prime number and $e \geq 1$ is an integer. In this paper, by means of generalized Reed-Solomon (GRS) codes, we construct two new classes of quantum…
Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two…
Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary…
There are two classes of quantum integrable systems on a manifold with quadratic integrals, the Liouville and the Lie integrable systems as it happens in the classical case. The quantum Liouville quadratic integrable systems are defined on…
We investigate the class of completely regular codes in graphs with a distance partition C_0,..., C_\rho, where each set C_i, for 0<=i<=r-1, is an independent set. This work focuses on the existence problem for such codes in the…
We show that unrolled quantum groups at odd roots of unity give rise to relative modular categories. These are the main building blocks for the construction of 1+1+1-TQFTs extending CGP invariants, which are non-semisimple quantum…
We give a procedure for "reverse engineering" a closed, simply connected, Riemannian manifold with bounded local geometry from a sparse chain complex over $\mathbb{Z}$. Applying this procedure to chain complexes obtained by "lifting"…
We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…