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Article Dans Une Revue Physical Review Research Année : 2023

Optimality conditions for spatial search with multiple marked vertices

Résumé

We contribute to fulfill the long-lasting gap in the understanding of the spatial search with multiple marked vertices. The theoretical framework is that of discrete-time quantum walks (QW), i.e., local unitary matrices that drive the evolution of a single particle on the lattice. QW based search algorithms are well understood when they have to tackle the fundamental problem of finding only one marked element in a d-dimensional grid and it has been proven they provide a quadratic advantage over classical searching protocols. However, once we consider searching more than one element, the behavior of the algorithm may be affected by the spatial configuration of the marked elements and even the quantum advantage is no longer guaranteed. Here our main contribution is threefold: (i) we provide sufficient conditions for optimality for a multi-items QWSearch algorithm; (ii) we provide analytical evidence that almost, but not all spatial configurations with multiple marked elements are optimal; and (iii) we numerically show that the computational advantage with respect to the classical counterpart is not always certain and it does depend on the proportion of searched elements over the total number of grid points
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Dates et versions

hal-04523921 , version 1 (27-03-2024)

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Mathieu Roget, Hachem Kadri, Giuseppe Di Molfetta. Optimality conditions for spatial search with multiple marked vertices. Physical Review Research, 2023, 5 (3), pp.033021. ⟨10.1103/PhysRevResearch.5.033021⟩. ⟨hal-04523921⟩
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