A quantum Jensen-Shannon graph kernel for unattributed graphs

Lu Bai, Luca Rossi, Andrea Torsello, Edwin R. Hancock

Research output: Journal article publicationJournal articleAcademic researchpeer-review

80 Citations (Scopus)


In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) [27,28] to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.

Original languageEnglish
Pages (from-to)344-355
Number of pages12
JournalPattern Recognition
Issue number2
Publication statusPublished - 1 Feb 2015
Externally publishedYes


  • Continuous-time quantum walk
  • Graph kernels
  • Quantum Jensen-Shannon divergence
  • Quantum state

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


Dive into the research topics of 'A quantum Jensen-Shannon graph kernel for unattributed graphs'. Together they form a unique fingerprint.

Cite this