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Communication Dans Un Congrès Année : 2023

Quantum Distance Calculation for ε-Graph Construction

Résumé

In machine learning and particularly in topological data analysis, ε-graphs are important tools but are generally hard to compute as the distance calculation between n points takes time O(n^2) classically. Recently, quantum approaches for calculating distances between n quantum states have been proposed, taking advantage of quantum superposition and entanglement. We investigate the potential for quantum advantage in the case of quantum distance calculation for computing ε-graphs. We show that, relying on existing quantum multi-state SWAP test based algorithms, the query complexity for correctly identifying (with a given probability) that two points are not ε-neighbours is at least O(n^3 / ln n), showing that this approach, if used directly for ε-graph construction, does not bring a computational advantage when compared to a classical approach.
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Dates et versions

hal-04118977 , version 1 (06-06-2023)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

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Naomi Mona Chmielewski, Nina Amini, Paulin Jacquot, Joseph Mikael. Quantum Distance Calculation for ε-Graph Construction. IEEE Quantum Week 2023, Sep 2023, Washington, United States. ⟨10.1109/QCE57702.2023.00010⟩. ⟨hal-04118977⟩
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