Perfect transmission and parallel composition for quantum walks on graphs with two leads

• URL: http://arxiv.org/abs/2605.14640v1
• Date: Thu, 14 May 2026 09:57:12 GMT
• Title: Perfect transmission and parallel composition for quantum walks on graphs with two leads
• Abstract summary: We study continuous-time quantum walks on finite graphs with two leads.<n>We derive explicit formulae for the two-terminal scattering matrix in terms of characteristics of the finite graph and itsdeleted subgraphs.<n>This turns the search for graphs with prescribed transmission properties into a geometric vector-sum problem for smaller building blocks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study scattering for continuous-time quantum walks on finite graphs with two attached leads. We derive explicit formulae for the two-terminal scattering matrix in terms of characteristic polynomials of the finite graph and its vertex-deleted subgraphs. For real-weighted two-terminal graphs, we then introduce three real quantities, $μ_1$, $μ_2$, and $ν$, which are each additive under parallel composition of graphs. In these variables, perfect transmission at fixed momentum is characterized by the condition $μ_1=μ_2$ together with a hyperbola in the corresponding $(μ,ν)$-plane, whose points determine the transmission phase. This turns the search for graphs with prescribed transmission properties into a geometric vector-sum problem for smaller building blocks.

Related papers

• Directed Graph Topology Inference via Graph Filter Identification [54.541275287889164]
  We address the problem of inferring a directed network from nodal measurements generated by a graph convolutional filter.<n>A joint graph filter and topology identification algorithm is also proposed, which alternates between the aforementioned steps to offer improved sample complexity.
  arXiv  Detail & Related papers  (2026-06-25T18:25:57Z)
• Symmetric and Antisymmetric Quantum States from Graph Structure and Orientation [0.0]
  We prove that a graph state is fully symmetric under particle permutations if and only if the underlying graph is complete.<n>We show that complete directed graphs endowed with appropriate orientations, for an odd number of qudits generate fully antisymmetric multipartite states.
  arXiv  Detail & Related papers  (2026-01-27T18:12:52Z)
• A discrete Benamou-Brenier formulation of Optimal Transport on graphs [3.076702179889855]
  We derive a discrete analogue of the Benamou-Brenier formulation for Wasserstein-$1$ distance on a graph and as a result classify all $W_$1$ geodesics on graphs.
  arXiv  Detail & Related papers  (2026-01-07T18:59:07Z)
• Pulsation of quantum walk between two arbitrary graphs with weakly connected bridge [0.0]
  We consider the Grover walk on a finite graph composed of two arbitrary simple graphs connected by one edge.<n>For sufficiently small values of $$, a phenomenon called pulsation occurs.<n>The pulsation is characterized by the periodic transfer of the quantum walker between the two graphs.
  arXiv  Detail & Related papers  (2025-11-17T02:01:37Z)
• From Laplacian-to-Adjacency Matrix for Continuous Spins on Graphs [0.0]
  We show that the free energy at low and high temperature $T$ is determined by the spectrum of two crucial objects from graph theory.<n>For decorated lattices, the singular part of the free energy is governed by the Laplacian spectrum, whereas this is true for the full free energy only in the zero temperature limit.<n>Results for quantum spin models on a loopless graph are also presented.
  arXiv  Detail & Related papers  (2025-11-15T19:14:35Z)
• Real state transfer on edge perturbed graphs with generalized clusters [0.0]
  We study the existence of real state transfer in edge-perturbed graphs containing generalized clusters.<n>A central observation is that the evolution of certain quantum states depends solely on the local structure of the underlying graph.
  arXiv  Detail & Related papers  (2025-05-12T18:26:59Z)
• InstructG2I: Synthesizing Images from Multimodal Attributed Graphs [50.852150521561676]
  We propose a graph context-conditioned diffusion model called InstructG2I. InstructG2I first exploits the graph structure and multimodal information to conduct informative neighbor sampling. A Graph-QFormer encoder adaptively encodes the graph nodes into an auxiliary set of graph prompts to guide the denoising process.
  arXiv  Detail & Related papers  (2024-10-09T17:56:15Z)
• Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs [131.53471236405628]
  We present three methods that exploit the induced graphon representation of graphs and graph signals on partitions of [0, 1]2 in the graphon space. We prove that those low dimensional representations constitute a convergent sequence of graphs and graph signals. We observe that graphon pooling performs significantly better than other approaches proposed in the literature when dimensionality reduction ratios between layers are large.
  arXiv  Detail & Related papers  (2022-12-15T22:11:34Z)
• Pseudo-Euclidean Attract-Repel Embeddings for Undirected Graphs [73.0261182389643]
  Dot product embeddings take a graph and construct vectors for nodes such that dot products between two vectors give the strength of the edge. We remove the transitivity assumption by embedding nodes into a pseudo-Euclidean space. Pseudo-Euclidean embeddings can compress networks efficiently, allow for multiple notions of nearest neighbors each with their own interpretation, and can be slotted' into existing models.
  arXiv  Detail & Related papers  (2021-06-17T17:23:56Z)
• Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs [62.997667081978825]
  We identify conditions which allow one to lift one dimensional solutions to solutions on graphs. We show that even for a simple example of a topologically interesting graph the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z-graded graph.
  arXiv  Detail & Related papers  (2020-08-11T17:58:13Z)
• Wasserstein-based Graph Alignment [56.84964475441094]
  We cast a new formulation for the one-to-many graph alignment problem, which aims at matching a node in the smaller graph with one or more nodes in the larger graph. We show that our method leads to significant improvements with respect to the state-of-the-art algorithms for each of these tasks.
  arXiv  Detail & Related papers  (2020-03-12T22:31:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.