Related papers: Transitivity of Varietal Hypercube Networks
The primary objective of this paper is to conduct a comparative analysis between two Machine Learning approaches: Tensor Networks (TN) and Variational Quantum Classifiers (VQC). While both approaches share similarities in their…
Variational Quantum Computing (VQC) faces fundamental scalability barriers, primarily due to barren plateaus and sensitivity to quantum noise. To address these challenges, we introduce TensorHyper-VQC, a novel tensor-train (TT)-guided…
Supercyclides are surfaces with a characteristic conjugate parametrization consisting of two families of conics. Patches of supercyclides can be adapted to a Q-net (a discrete quadrilateral net with planar faces) such that neighboring…
The complementary features of different qubit platforms for computing and communicating impose an intrinsic hardware heterogeneity in any quantum network, where nodes, while processing and storing quantum information, must also communicate…
Multivariate (MTV) porous materials exhibit unique structural complexities based on diverse spatial arrangements of multiple building block combinations. These materials possess potential synergistic functionalities that exceed the sum of…
Variational Quantum Circuits (VQC) are promising models for quantum machine learning, but standard monolithic architectures face an expressivity--trainability dilemma: small circuits can be under-parameterized, while larger circuits are…
The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. The $n$-dimensional twisted cube, denoted by $TQ_n$, an important variation of the hypercube, possesses some…
The $n$-dimensional hypercube $Q_n$ is a graph with vertex set $\{0,1\}^n$ such that there is an edge between two vertices if and only if they differ in exactly one coordinate. For any graph $H$, define $\text{ex}(Q_n,H)$ to be the maximum…
The balanced hypercube, $BH_n$, is a variant of hypercube $Q_n$. Zhou et al. [Inform. Sci. 300 (2015) 20-27] proposed an interesting problem that whether there is a fault-free Hamiltonian cycle in $BH_n$ with each vertex incident to at…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
We study the routing of quantum information in parallel on multi-dimensional networks of tunable qubits and oscillators. These theoretical models are inspired by recent experiments in superconducting circuits using Josephson junctions and…
Recently, the work on quantum automorphism groups of graphs has seen renewed progress, which we expand in this paper. Quantum symmetry is a richer notion of symmetry than the classical symmetries of a graph. In general, it is non-trivial to…
Modeling complex systems that consist of different types of objects leads to multilayer networks, where nodes in the different layers represent different kind of objects. Nodes are connected by edges, which have positive weights. A…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
In this paper we study the connectivity properties of the random subgraph of the $n$-cube generated by the $k$-out model and denoted by $Q^n(k)$. Let $k$ be an integer, $1\leq k \leq n-1$. We let $Q^n(k)$ be the graph that is generated by…
We describe overcommutative varieties of semigroups whose lattice of overcommutative subvarieties satisfies a non-trivial identity or quasiidentity. These two properties turn out to be equivalent.
Quantum channels are known to provide qualitatively better information transfer capacities over their classical counterparts. Examples include quantum cryptography, quantum dense coding, and quantum teleportation. This is a short review on…
In recent years, neural networks (NNs) have driven significant advances in machine learning. However, as tasks grow more complex, NNs often require large numbers of trainable parameters, which increases computational and energy demands.…
The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-size quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the…
Quantum transport of charge or energy in networks with discrete sites is central to diverse quantum technologies, from molecular electronics to light harvesting and quantum opto-mechanical metamaterials. A one dimensional network can be…