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Although RF fingerprinting is one of the most commonly used techniques for localization, deploying it in a ubiquitous manner requires addressing the challenge of supporting a large number of heterogeneous devices and their variations. We present QHFP, a device-independent quantum fingerprint matching algorithm that addresses two of the issues for realizing worldwide ubiquitous large-scale location tracking systems: storage space and running time as well as devices heterogeneity. In particular, we present a quantum algorithm with a complexity that is exponentially better than the classical techniques, both in space and running time. QHFP also has provisions for handling the inherent localization error due to building the large-scale fingerprint using heterogeneous devices. We give the details of the entire system starting from extracting device-independent features from the raw RSS, mapping the classical feature vectors to their quantum counterparts, and showing a quantum cosine similarity algorithm for fingerprint matching. We have implemented our quantum algorithm and deployed it in a real testbed using the IBM Quantum machine simulator. Results confirm the ability of QHFP to obtain the correct estimated location with an exponential improvement in space and running time compared to the traditional classical counterparts. In addition, the proposed device-independent features lead to more than 20% better accuracy in median error. This highlights the promise of our algorithm for future ubiquitous large-scale worldwide device-independent fingerprinting localization systems.