Related papers: Efficiently Controllable Graphs
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a…
The ability to implement any desired quantum logic gate on a quantum processing unit is equivalent to evolution-operator controllability of the qubits. Conversely, controllability analysis can be used to minimize the resources, i.e., the…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
In this paper, we propose to study on sufficient control of complex networks which is to control a sufficiently large portion of the network, where only the quantity of controllable nodes matters. To the best of our knowledge, this is the…
Let $G$ be a graph on $n$ vertices with adjacency matrix $A$, and let $\mathbf{1}$ be the all-ones vector. We call $G$ controllable if the set of vectors $\mathbf{1}, A\mathbf{1}, \dots, A^{n-1}\mathbf{1}$ spans the whole space…
In this paper, we develop a notion of controllability for hypergraphs via tensor algebra and polynomial control theory. Inspired by uniform hypergraphs, we propose a new tensor-based multilinear dynamical system representation, and derive a…
In quantum computing, the connectivity of qubits placed on two-dimensional chips limits the scalability and functionality of solid-state quantum computers. This paper presents two approaches to constructing complex quantum networks from…
The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to…
This letter deals with the controllability issue of complex networks. An index is chosen to quantitatively measure the extent of controllability of given network. The effect of this index is analyzed based on empirical studies on various…
Control of quantum operations is a crucial yet expensive construct for quantum computation. Efficient implementations of controlled operations often avoid applying control to certain subcircuits, which can significantly reduce the number of…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
Global control offers a promising route to scalable quantum computing. A recent conjecture by Hu et al. (arXiv:2508.19075) proposes that any connected qubit graph equipped with global Ising-type interactions and tunable global transverse…
Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…
In this paper we investigate the controllability and observability properties of a family of linear dynamical systems, whose structure is induced by the Laplacian of a grid graph. This analysis is motivated by several applications in…
We study the transport efficiency of excitations on complex quantum networks with loops. For this we consider sequentially growing networks with different topologies of the sequential subgraphs. This can lead either to a universal complete…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
An efficient dominating set (or perfect code) in a graph is a set of vertices the closed neighborhoods of which partition the vertex set of the graph. The minimum weight efficient domination problem is the problem of finding an efficient…