# Spatial search by continuous-time quantum walk with multiple marked vertices

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## Abstract

In the typical spatial search problems solved by continuous-time quantum walk, changing the location of the marked vertices does not alter the search problem. In this paper, we consider search when this is no longer true. In particular, we analytically solve search on the “simplex of \(K_M\) complete graphs” with all configurations of two marked vertices, two configurations of \(M+1\) marked vertices, and two configurations of \(2(M+1)\) marked vertices, showing that the location of the marked vertices can dramatically influence the required jumping rate of the quantum walk, such that using the wrong configuration’s value can cause the search to fail. This sensitivity to the jumping rate is an issue unique to continuous-time quantum walks that does not affect discrete-time ones.

## Keywords

Grover’s algorithm Quantum search Spatial search Quantum random walk Multiple marked vertices## Notes

### Acknowledgments

Thanks to Andris Ambainis for useful discussions. This work was supported by the European Union Seventh Framework Programme (FP7/2007–2013) under the QALGO (Grant Agreement No. 600700) project, and the ERC Advanced Grant MQC.

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