An Efficient Quantum Euclidean Similarity Algorithm for Worldwide Localization

Fingerprinting techniques are widely used for localization because of their accuracy, especially in the presence of wireless channel noise. However, the fingerprinting techniques require significant storage and running time, which is a concern when implementing such systems on a global worldwide scale. In this paper, we propose an efficient quantum Euclidean similarity algorithm for wireless localization systems. The proposed quantum algorithm offers exponentially improved complexity compared to its classical counterpart and even the state-of-the-art quantum localization systems, in terms of both storage space and running time. The basic idea is to entangle the test received signal strength (RSS) vector with the fingerprint vectors at different locations and perform the similarity calculation in parallel to all fingerprint locations. We give the details of how to construct the quantum fingerprint, how to encode the RSS measurements in quantum particles, and finally; present the quantum algorithm for calculating the Euclidean similarity between the online RSS measurements and the fingerprint ones. Implementation and evaluation of our algorithm in a real testbed using a real IBM quantum machine as well as a simulation for a larger testbed confirm its ability to correctly obtain the estimated location with an exponential enhancement in both time and space compared to the traditional classical fingerprinting techniques and the state-of-the-art quantum localization techniques.