# Quantum graph walks II: Quantum walks on graph coverings

@article{Higuchi2012QuantumGW, title={Quantum graph walks II: Quantum walks on graph coverings}, author={Yusuke Higuchi and N. Konno and I. Sato and E. Segawa}, journal={arXiv: Mathematical Physics}, year={2012} }

We give a new determinant expression for the characteristic polynomial of the bond scattering matrix of a quantum graph G. Also, we give a decomposition formula for the characteristic polynomial of the bond scattering matrix of a regular covering of G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we express the characteristic polynomial of the bond scattering matrix of a regular covering of G by means of its L-functions. As an applicationâ€¦Â Expand

#### 2 Citations

Unitary equivalent classes of one-dimensional quantum walks

- Physics, Computer Science
- Quantum Inf. Process.
- 2016

#### References

SHOWING 1-10 OF 41 REFERENCES

Quantum walks, Ihara zeta functions and cospectrality in regular graphs

- Mathematics, Computer Science
- Quantum Inf. Process.
- 2011

A Matrix Representation of Graphs and its Spectrum as a Graph Invariant

- Physics, Mathematics
- Electron. J. Comb.
- 2006

On the relation between quantum walks and zeta functions

- Mathematics, Computer Science
- Quantum Inf. Process.
- 2012