Spatial search in a honeycomb network
G. Abal, R. Donangelo, F.L. Marquezino, R. Portugal

TL;DR
This paper presents a quantum algorithm for spatial search on a honeycomb lattice, achieving a time complexity of O(√N log N) using a modified quantum walk, advancing quantum search methods on non-square networks.
Contribution
It introduces a novel quantum walk-based search algorithm specifically designed for honeycomb networks, extending quantum search techniques to hexagonal lattice structures.
Findings
Quantum search on honeycomb lattice has complexity O(√N log N)
Modified quantum walk effectively explores hexagonal networks
Framework adapts quantum search to non-square geometries
Abstract
The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighboring sites are allowed. In this paper, a quantum algorithm for the spatial search problem on a honeycomb lattice with sites and torus-like boundary conditions. The search algorithm is based on a modified quantum walk on a hexagonal lattice and the general framework proposed by Ambainis, Kempe and Rivosh is used to show that the time complexity of this quantum search algorithm is .
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