Spatial quantum search in a triangular network

TL;DR

This paper introduces a quantum algorithm for spatial search on a triangular lattice, achieving a time complexity of O(√(N log N)), extending quantum search techniques to this specific network topology.

Contribution

It adapts the AKR-Tulsi quantum search framework to a triangular lattice, providing a specialized algorithm with proven efficiency for this network structure.

Findings

Quantum search on a triangular lattice has complexity O(√(N log N))

The algorithm extends existing quantum search frameworks to new network topologies

Efficient spatial search is feasible on triangular networks with boundary conditions

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. We propose a quantum algorithm for the spatial search problem on a triangular lattice with N sites and torus-like boundary conditions. The proposed algortithm is a special case of the general framework for abstract search proposed by Ambainis, Kempe and Rivosh [AKR05] (AKR) and Tulsi [Tulsi08], applied to a triangular network. The AKR-Tulsi formalism was employed to show that the time complexity of the quantum search on the triangular lattice is O(sqrt(N logN)).