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A Quantum Jensen-Shannon Graph Kernel Using Discrete-Time Quantum Walks

  • Lu Bai
  • Luca Rossi
  • Peng Ren
  • Zhihong Zhang
  • Edwin R. Hancock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9069)

Abstract

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Keywords

Density Matrix Line Graph Original Graph Quantum Walk Graph Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Lu Bai
    • 1
    • 2
  • Luca Rossi
    • 3
  • Peng Ren
    • 4
  • Zhihong Zhang
    • 5
  • Edwin R. Hancock
    • 2
  1. 1.School of InformationCentral University of Finance and EconomicsBeijingChina
  2. 2.Department of Computer ScienceUniversity of YorkYorkUK
  3. 3.School of Computer ScienceUniversity of BirminghamBirminghamUK
  4. 4.College of Information and Control EngineeringChina University of Petroleum (Huadong)QingdaoP.R. China
  5. 5.Software schoolXiamen UniversityFujianChina

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