Related papers: Quantum max-flow in the bridge graph
The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a…
The max-flow min-cut theorem is a cornerstone result in combinatorial optimization. Calegari et al. (arXiv:0802.3208) initialized the study of quantum max-flow min-cut conjecture, which connects the rank of a tensor network and the min-cut.…
The quantum max-flow min-cut conjecture relates the rank of a tensor network to the minimum cut in the case that all tensors in the network are identical\cite{mfmc1}. This conjecture was shown to be false in Ref. \onlinecite{mfmc2} by an…
We propose to study maximum flow problems for connectome graphs. We suggest a few computational problems: finding vertex pairs with maximal flow, finding new edges which would increase the maximal flow. Initial computation results for some…
We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.
In this paper, we study the mean curvature flow of graphs with Neumann boundary condition. The main aim is to use the maximum principle to get the boundary gradient estimate for solutions. In particular, we obtain the corresponding…
The problem of sending the maximum amount of flow $q$ between two arbitrary nodes $s$ and $t$ of complex networks along links with unit capacity is studied, which is equivalent to determining the number of link-disjoint paths between $s$…
Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which…
We study the phenomenon of quantum backflow in tight-binding systems with complex couplings, considering different boundary conditions and lattice sizes. Backflow is an intrinsically non-classical effect where the density flux associated…
This work deals with quantum transport in open quantum graphs. We consider the case of complete graphs on $n$ vertices with an edge removed and attached to two leads, to represent the entrance and exit channels, from where we calculate the…
This paper considers a problem of quantum communication between parties that are connected through a network of quantum channels. The model in this paper assumes that there is no prior entanglement shared among any of the parties, but that…
Quantum walks have frequently envisioned the behavior of a quantum state traversing a classically defined, generally finite, graph structure. While this approach has already generated significant results, it imposes a strong assumption: all…
With a growing number of quantum networks in operation, there is a pressing need for performance analysis of quantum switching technologies. A quantum switch establishes, distributes, and maintains entanglements across a network. In…
By revisiting the Kirchhoff's Matrix-Tree Theorem, we give an exact formula for the number of spanning trees of a graph in terms of the quantum relative entropy between the maximally mixed state and another state specifically obtained from…
We discover the quantum analog of the well-known classical maximum power transfer theorem. Our theoretical framework considers the continuous steady-state problem of coherent energy transfer through an N-node bosonic network coupled to an…
Highly efficient transfer of quantum resources including quantum excitations, states, and information on quantum networks is an important task in quantum information science. Here, we propose a bipartite-graph framework for studying quantum…
The conditions under which entanglement becomes maximal are sought in the general one--dimensional quantum random walk with two walkers. Moreover, a one--dimensional shift operator for the two walkers is introduced and its performance in…
The quantum graph plays the role of a solvable model for a two-dimensional network. Here fitting parameters of the quantum graph for modelling the junction is discussed, using previous results of the second author.