Relation between quantum walks with tails and quantum walks with sinks on finite graphs

• URL: http://arxiv.org/abs/2105.03111v1
• Date: Fri, 7 May 2021 08:31:06 GMT
• Title: Relation between quantum walks with tails and quantum walks with sinks on finite graphs
• Authors: Norio Konno, Etsuo Segawa, Martin \v{S}tefa\v{n}\'ak
• Abstract summary: We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails. The centered eigenspace of the Grover walk is the attractor eigenspace of the Grover walk with sinks. It is described by the persistent eigenspace of the underlying random walk whose support has no overlap to the boundaries of the graph and combinatorial flow in the graph theory.

Related papers

• Discrete-time quantum walks on Cayley graphs of Dihedral groups using generalized Grover coins [0.0]
  We study discrete-time quantum walks on Cayley graphs corresponding to Dihedral groups. We show that the walks are periodic only for coins that are permutation or negative of a permutation matrix.
  arXiv  Detail & Related papers  (2023-09-26T18:53:35Z)
• Dual Node and Edge Fairness-Aware Graph Partition [25.808586461486932]
  We propose a notion edge balance to measure the proportion of edges connecting different demographic groups in clusters. We validate our framework through several social network datasets and observe balanced partition in terms of both nodes and edges along with good utility.
  arXiv  Detail & Related papers  (2023-06-16T18:18:37Z)
• Cat-qubit-inspired gate on cos($2\theta$) qubits [77.34726150561087]
  We introduce a single-qubit $Z$ gate inspired by the noise-bias preserving gate of the Kerr-cat qubit. This scheme relies on a $pi$ rotation in phase space via a beamsplitter-like transformation between a qubit and ancilla qubit.
  arXiv  Detail & Related papers  (2023-04-04T23:06:22Z)
• Periodicity of bipartite walk on biregular graphs with conditional spectra [0.0]
  We study a class of discrete quantum walks, known as bipartite walks. Any discrete quantum walk is given by the powers of a unitary matrix $U$ indexed by arcs or edges of the underlying graph. We apply periodicity results of bipartite walks to get a characterization of periodicity of Grover's walk on regular graphs.
  arXiv  Detail & Related papers  (2022-11-04T21:02:30Z)
• Quantitative approach to Grover's quantum walk on graphs [62.997667081978825]
  We study Grover's search algorithm focusing on continuous-time quantum walk on graphs. Instead of finding specific graph topologies convenient for the related quantum walk, we fix the graph topology and vary the underlying graph endowed Laplacians.
  arXiv  Detail & Related papers  (2022-07-04T19:33:06Z)
• A comfortable graph structure for Grover walk [0.0]
  We consider a Grover walk model on a finite internal graph, which is connected with a finite number of semi-infinite length paths. We give some characterization upon the scattering of the stationary state on the surface of the internal graph. We introduce a comfortability function of a graph for the quantum walk, which shows how many walkers can stay in the interior.
  arXiv  Detail & Related papers  (2022-01-06T05:29:50Z)
• Odd-periodic Grover walk [0.0]
  We investigate the relationship between the quantum walk and the underlying graph, focusing on the characterization of graphs exhibiting a periodic Grover walk. It is expected that graphs exhibiting a periodic Grover walk with odd period correspond to cycles with odd length. We address that problem and are able to perfectly characterize the class of graphs exhibiting an odd-periodic Grover walk by using a method.
  arXiv  Detail & Related papers  (2021-06-12T08:02:25Z)
• Walk/Zeta Correspondence [0.0]
  This paper extends these walks to a class of walks including random walks, correlated random walks, quantum walks, and open quantum random walks on the torus by the Fourier analysis.
  arXiv  Detail & Related papers  (2021-04-21T00:17:54Z)
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space [62.997667081978825]
  We investigate a quantum system simultaneously exposed to two structured reservoirs. We employ a numerically exact quasi-2D tensor network combining both diagonal and off-diagonal system-reservoir interactions with a twofold memory for continuous and discrete retardation effects. As a possible example, we study the non-Markovian interplay between discrete photonic feedback and structured acoustic phononovian modes, resulting in emerging inter-reservoir correlations and long-living population trapping within an initially-excited two-level system.
  arXiv  Detail & Related papers  (2020-11-10T12:38:35Z)
• Continuous-time quantum walks in the presence of a quadratic perturbation [55.41644538483948]
  We address the properties of continuous-time quantum walks with Hamiltonians of the form $mathcalH= L + lambda L2$. We consider cycle, complete, and star graphs because paradigmatic models with low/high connectivity and/or symmetry.
  arXiv  Detail & Related papers  (2020-05-13T14:53:36Z)
• Gated Graph Recurrent Neural Networks [176.3960927323358]
  We introduce Graph Recurrent Neural Networks (GRNNs) as a general learning framework for graph processes. To address the problem of vanishing gradients, we put forward GRNNs with three different gating mechanisms: time, node and edge gates. The numerical results also show that GRNNs outperform GNNs and RNNs, highlighting the importance of taking both the temporal and graph structures of a graph process into account.
  arXiv  Detail & Related papers  (2020-02-03T22:35:14Z)

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.