Related papers: Quantum max-flow in the bridge graph
In this paper, we determine a formula for Kemeny's constant for a graph with multiple bridges, in terms of quantities that are inherent to the subgraphs obtained upon removal of all bridges and that can be computed independently. With the…
The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform…
In this short paper, we propose a new multi-fractal flow model, aiming to provide a possible explanation for the crossover phenomena that appear in the estimation of Hurst exponent for network traffic. It is shown that crossover occurs if…
We report a method that exploits a connection between quantum contextuality and graph theory to reveal any form of quantum contextuality in high-precision experiments. We use this technique to identify a graph which corresponds to an…
We consider the capacity problem for wireless networks. Networks are modeled as random unit-disk graphs, and the capacity problem is formulated as one of finding the maximum value of a multicommodity flow. In this paper, we develop a proof…
Existing quantum routing implicitly mimics classical routing principles, with finding the ``best'' path (aka pathfinding), according to a selected routing metric, as a core mechanism for establishing end-to-end entanglement. However,…
It is proposed two models describing transport and absorbtion processes that occur in nanoscale fragments of electrical circuits, pulled adsorbed molecules, atomic or molecular chains connecting electrodes. Discrete chain model of a…
We consider a model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly between document transfers. We study critical fluid models obtained as formal…
We consider the problem of multi-path entanglement distribution to a pair of nodes in a quantum network consisting of devices with non-deterministic entanglement swapping capabilities. Multi-path entanglement distribution enables a network…
The flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions. We extend this idea to the quantum realm and introduce the Quantum Flow…
The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global…
Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers' car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a…
This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…
We examine quantum transport in periodic quantum graphs with a vertex coupling non-invariant with respect to time reversal. It is shown that the graph topology may play a decisive role in the conductivity properties illustrating this claim…
For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with an end-to-end practical applications -- in this instance, fluid dynamics. We debut here a high performance…
Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied…
We introduce a new graph invariant \Lambda(G) that we call maxmaxflow, and put it in the context of some other well-known graph invariants, notably maximum degree and its relatives. We prove the equivalence of two "dual" definitions of…
We discuss quantum capacities for two types of entanglement networks: $\mathcal{Q}$ for the quantum repeater network with free classical communication, and $\mathcal{R}$ for the tensor network as the rank of the linear operation represented…
A continuous-time quantum walk on a graph $X$ is represented by the complex matrix $\exp (-\mathrm{i} t A)$, where $A$ is the adjacency matrix of $X$ and $t$ is a non-negative time. If the graph models a network of interacting qubits,…
The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is…