Related papers: Constructing Two Edge-Disjoint Hamiltonian Cycles …

There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…

This paper considers the conditional fault tolerance, $h$-super connectivity $\kappa^{h}$ and $h$-super edge-connectivity $\lambda^{h}$ of the hierarchical cubic network $HCN_n$, an attractive alternative network to the hypercube, and shows…

We prove that local random quantum circuits acting on n qubits composed of O(t^{10} n^2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design…

A graph $G$ is $l$-path Hamiltonian if every path of length not exceeding $l$ is contained in a Hamiltonian cycle. It is well known that a 2-connected, $k$-regular graph $G$ on at most $3k-1$ vertices is edge-Hamiltonian if for every edge…

This paper introduces a new variant of hypercubes, which we call Z-cubes. The n-dimensional Z-cube $H_n$ is obtained from two copies of the (n-1)-dimensional Z-cube $H_{n-1}$ by adding a special perfect matching between the vertices of…

The square of a graph is obtained by adding additional edges joining all pair of vertices of distance two in the original graph. Particularly, if $C$ is a hamiltonian cycle of a graph $G$, then the square of $C$ is called a hamiltonian…

Token ring topology has been frequently used in the design of distributed loop computer networks and one measure of its performance is the diameter. We propose an algorithm for constructing hamiltonian graphs with $n$ vertices and maximum…

Connectivity is a cornerstone concept in graph theory, essential for evaluating the robustness of networks against failures. To better capture fault tolerance in complex systems, researchers have extended classical connectivity notions, one…

We show a relation, based on parallel repetition of the Magic Square game, that can be solved, with probability exponentially close to $1$ (worst-case input), by $1D$ (uniform) depth $2$, geometrically-local, noisy (noise below a…

A long-standing conjecture of Kelly states that every regular tournament on n vertices can be decomposed into (n-1)/2 edge-disjoint Hamilton cycles. We prove this conjecture for large n. In fact, we prove a far more general result, based on…

We prove that there is a trade-off relation between the entanglement cost and the number of rounds of communication, for two distant parties to accomplish a bidirectional quantum information task by local operations and classical…

This paper summarizes and extends the authors' work on the bifurcation of topologically protected edge states in continuous two-dimensional honeycomb structures. We consider a family of Schr\"odinger Hamiltonians consisting of a bulk…

In this paper we prove a sufficient condition for the existence of a Hamilton cycle, which is applicable to a wide variety of graphs, including relatively sparse graphs. In contrast to previous criteria, ours is based on only two…

Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to…

This thesis captures the ongoing development of twisted cubes, which is a modification of cubes (in a topological sense) where its homotopy type theory does not require paths or higher paths to be invertible. My original motivation to…

Networks of interacting nodes connected by edges arise in almost every branch of scientific enquiry. The connectivity structure of the network can force the existence of invariant subspaces, which would not arise in generic dynamical…

In this work we use the concept of quantum fingerprinting to develop a quantum communication protocol in the simultaneous message passing model that calculates the Hamming distance between two $n$-bit strings up to relative error…

Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. One of the most efficient interconnection networks is the hypercube due to its structural regularity, potential…

The cycles in an interconnection network are one of the communication types that are considered as a factor to measure the efficiency and reliability of the networks' topology. The network is said to be panconnected if there are cycles of…

Near-term quantum computers are primarily limited by errors in quantum operations (or gates) between two quantum bits (or qubits). A physical machine typically provides a set of basis gates that include primitive 2-qubit (2Q) and 1-qubit…