Laplacian versus adjacency matrix in quantum walk search

@article{Wong2016LaplacianVA,
  title={Laplacian versus adjacency matrix in quantum walk search},
  author={Thomas G. Wong and Lu{\'i}s Tarrataca and Nikolay Nahimov},
  journal={Quantum Information Processing},
  year={2016},
  volume={15},
  pages={4029-4048}
}
  • Thomas G. Wong, Luís Tarrataca, Nikolay Nahimov
  • Published 2016
  • Computer Science, Physics
  • Quantum Information Processing
  • A quantum particle evolving by Schrödinger’s equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace’s operator. In discrete space, this is replaced by the discrete or graph Laplacian, which gives rise to a continuous-time quantum walk. Besides this natural definition, some quantum walk algorithms instead use the adjacency matrix to effect the walk. While this is equivalent to the Laplacian for regular graphs, it is different for non-regular… CONTINUE READING

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