Abstract
The concept of lackadaisical quantum walk – quantum walk with self loops – was first introduced for discrete-time quantum walk on one-dimensional line [8]. Later it was successfully applied to improve the running time of the spacial search on two-dimensional grid [16].
In this paper we study search by lackadaisical quantum walk on the two-dimensional grid with multiple marked vertices. First, we show that the lackadaisical quantum walk, similarly to the regular (non-lackadaisical) quantum walk, has exceptional configuration, i.e. placements of marked vertices for which the walk has no speed-up over the classical exhaustive search. Next, we demonstrate that the weight of the self-loop suggested in [16] is not optimal for multiple marked vertices. And, last, we show how to adjust the weight of the self-loop to overcome the aforementioned problem.
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Notes
- 1.
The numerical results in [16] show that probability of finding a marked vertex is close to 1 and approaches 1 as N goes to infinity.
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Nahimovs, N. (2019). Lackadaisical Quantum Walks with Multiple Marked Vertices. In: Catania, B., Královič, R., Nawrocki, J., Pighizzini, G. (eds) SOFSEM 2019: Theory and Practice of Computer Science. SOFSEM 2019. Lecture Notes in Computer Science(), vol 11376. Springer, Cham. https://doi.org/10.1007/978-3-030-10801-4_29
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DOI: https://doi.org/10.1007/978-3-030-10801-4_29
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