Laplacian State Transfer on Graphs with an Edge Perturbation Between Twin Vertices

• URL: http://arxiv.org/abs/2109.05306v1
• Date: Sat, 11 Sep 2021 15:48:18 GMT
• Title: Laplacian State Transfer on Graphs with an Edge Perturbation Between Twin Vertices
• Authors: Hiranmoy Pal
• Abstract summary: We consider quantum state transfer relative to the Laplacian matrix of a graph. We investigate the existence of quantum state transfer between a pair of twin vertices in a graph when the edge between the vertices is perturbed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider quantum state transfer relative to the Laplacian matrix of a graph. Let $N(u)$ denote the set of all neighbors of a vertex $u$ in a graph $G$. A pair of vertices $u$ and $v$ are called twin vertices of $G$ provided $N(u)\setminus\{v \}=N(v)\setminus\{u \}$. We investigate the existence of quantum state transfer between a pair of twin vertices in a graph when the edge between the vertices is perturbed. We find that removal of any set of pairwise non-adjacent edges from a complete graph with a number of vertices divisible by $4$ results Laplacian perfect state transfer (or LPST) at $\frac{\pi}{2}$ between the end vertices of every edge removed. Further, we show that all Laplacian integral graphs with a pair of twin vertices exhibit LPST when the edge between the vertices is perturbed. In contrast, we conclude that LPST can be achieved in every complete graph between the end vertices of any number of suitably perturbed non-adjacent edges. The results are further generalized to obtain a family of edge perturbed circulant graphs exhibiting Laplacian pretty good state transfer (or LPGST) between twin vertices. A subfamily of which is also identified to admit LPST at $\frac{\pi}{2}$.

Related papers

• Two-state transfer: a generalization of pair and plus state transfer [0.0]
  A two-state in a graph $X$ is a quantum state of the form $mathbfe_u+smathbfe_v$. We investigate quantum state transfer between two-states, where the Hamiltonian is taken to be the adjacency, Laplacian or signless Laplacian matrix of the graph.
  arXiv  Detail & Related papers  (2024-04-25T14:45:49Z)
• Quantum walks on join graphs [0.0]
  We explore the behaviour of a continuous quantum walk on a weighted join graph having the adjacency matrix or Laplacian matrix as its associated Hamiltonian. We characterize strong cospectrality, periodicity and perfect state transfer (PST) in a join graph. We demonstrate that the bound $frac2|V(X)|$ is tight for infinite families of graphs.
  arXiv  Detail & Related papers  (2023-12-12T00:33:30Z)
• Quantum walks on blow-up graphs [0.0]
  A blow-up of $n$ copies of a graph $G$ is the graph $oversetnuplusG$. We investigate the existence of quantum state transfer on a blow-up graph $oversetnuplusG$.
  arXiv  Detail & Related papers  (2023-08-26T14:07:25Z)
• Detection of Dense Subhypergraphs by Low-Degree Polynomials [72.4451045270967]
  Detection of a planted dense subgraph in a random graph is a fundamental statistical and computational problem. We consider detecting the presence of a planted $Gr(ngamma, n-alpha)$ subhypergraph in a $Gr(n, n-beta) hypergraph. Our results are already new in the graph case $r=2$, as we consider the subtle log-density regime where hardness based on average-case reductions is not known.
  arXiv  Detail & Related papers  (2023-04-17T10:38:08Z)
• Efficient Signed Graph Sampling via Balancing & Gershgorin Disc Perfect Alignment [51.74913666829224]
  We show that for datasets with strong inherent anti-correlations, a suitable graph contains both positive and negative edge weights. We propose a linear-time signed graph sampling method centered on the concept of balanced signed graphs. Experimental results show that our signed graph sampling method outperformed existing fast sampling schemes noticeably on various datasets.
  arXiv  Detail & Related papers  (2022-08-18T09:19:01Z)
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States [77.34726150561087]
  We show how all properties of a quantum manifold of states are fully described by a gauge-invariant Bargmann. We show how our results have immediate applications to the modern theory of polarization.
  arXiv  Detail & Related papers  (2022-05-30T18:01:34Z)
• Universality of the fully connected vertex in Laplacian continuous-time quantum walk problems [0.0]
  We prove that the continuous-time quantum walk (CTQW) -- with Hamiltonian $H=gamma L$ -- does not depend on the graph $G$. We apply our results to spatial search and quantum transport for single and multiple fully connected marked vertices.
  arXiv  Detail & Related papers  (2022-02-28T14:33:44Z)
• $n$-qubit states with maximum entanglement across all bipartitions: A graph state approach [0.0]
  We show that a subset of the 'graph states' satisfy this condition, hence providing a recipe for constructing $k$-uniform states. Finding recipes for construction of $k$-uniform states using graph states is useful since every graph state can be constructed starting from a product state.
  arXiv  Detail & Related papers  (2022-01-14T19:00:09Z)
• Accelerated Primal-Dual Gradient Method for Smooth and Convex-Concave Saddle-Point Problems with Bilinear Coupling [84.47780064014262]
  We study a linear convex-concave saddle-point problem $min_xmax_y f(x) ytopmathbfA x - g(y)
  arXiv  Detail & Related papers  (2021-12-30T20:31:46Z)
• Projection-free Graph-based Classifier Learning using Gershgorin Disc Perfect Alignment [59.87663954467815]
  In graph-based binary learning, a subset of known labels $hatx_i$ are used to infer unknown labels. When restricting labels $x_i$ to binary values, the problem is NP-hard. We propose a fast projection-free method by solving a sequence of linear programs (LP) instead.
  arXiv  Detail & Related papers  (2021-06-03T07:22:48Z)
• Accelerated Gradient Tracking over Time-varying Graphs for Decentralized Optimization [77.57736777744934]
  This paper revisits and extends the widely used accelerated gradient tracking. Our complexities improve significantly on the ones of $cal O(frac1epsilon5/7)$ and $cal O(fracLmu)5/7frac1 (1-sigma)1.5logfrac1epsilon)$.
  arXiv  Detail & Related papers  (2021-04-06T15:34:14Z)

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.