# 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} }

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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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 25 REFERENCES

## Faster quantum walk search on a weighted graph

VIEW 3 EXCERPTS

## Connectivity is a poor indicator of fast quantum search.

VIEW 1 EXCERPT

## Grover Search with Lackadaisical Quantum Walks

VIEW 2 EXCERPTS

## Global symmetry is unnecessary for fast quantum search

VIEW 5 EXCERPTS

## Perfect state transfer in Laplacian quantum walk

VIEW 1 EXCERPT

## Spatial search by quantum walk

VIEW 6 EXCERPTS

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## Exponential algorithmic speedup by a quantum walk

VIEW 1 EXCERPT