  Effective access points (APs) selection is a crucial step in localization
systems. It directly affects both localization accuracy and computational
efficiency. Classical APs selection algorithms are usually computationally
expensive, hindering the deployment of localization systems in a large
worldwide scale.
  In this paper, we introduce a quantum APs selection algorithm for large-scale
localization systems. The proposed algorithm leverages quantum annealing to
eliminate redundant and noisy APs. We explain how to formulate the APs
selection problem as a quadratic unconstrained binary optimization (QUBO)
problem, suitable for quantum annealing, and how to select the minimum number
of APs that maintain the same overall localization system accuracy as the
complete APs set. Based on this, we further propose a logarithmic-complexity
algorithm to select the optimal number of APs.
  We implement our quantum algorithm on a real D-Wave Systems quantum machine
and assess its performance in a real test environment for a floor localization
problem. Our findings reveal that by selecting fewer than 14% of the available
APs in the environment, our quantum algorithm achieves the same floor
localization accuracy as utilizing the entire set of APs and a superior
accuracy over utilizing the reduced dataset by classical APs selection
counterparts. Moreover, the proposed quantum algorithm achieves more than an
order of magnitude speedup over the corresponding classical APs selection
algorithms, emphasizing the efficiency of the proposed quantum algorithm for
large-scale localization systems.
