6533b7d1fe1ef96bd125ceb1
RESEARCH PRODUCT
Spatial Search by Continuous-Time Quantum Walk with Multiple Marked Vertices
Thomas G. Wongsubject
Quantum PhysicsSimplexSpatial searchFOS: Physical sciencesStatistical and Nonlinear Physicsmedicine.disease_cause01 natural sciences010305 fluids & plasmasTheoretical Computer ScienceElectronic Optical and Magnetic MaterialsCombinatoricsJumpingModeling and Simulation0103 physical sciencesSignal ProcessingmedicineSearch problemQuantum walkContinuous-time quantum walkSensitivity (control systems)Electrical and Electronic Engineering010306 general physicsQuantum Physics (quant-ph)Mathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-28 |