Quantum Distance Calculation for $\epsilon$-Graph Construction

• URL: http://arxiv.org/abs/2306.04290v1
• Date: Wed, 7 Jun 2023 09:43:28 GMT
• Title: Quantum Distance Calculation for $\epsilon$-Graph Construction
• Authors: Naomi Mona Chmielewski (EDF R&D OSIRIS, L2S), Nina Amini (CNRS, L2S), Paulin Jacquot (EDF R&D OSIRIS), Joseph Mikael (EDF R&D OSIRIS)
• Abstract summary: We investigate the potential for quantum advantage in the case of quantum distance calculation for computing $epsilon$-graphs. We show that, relying on existing quantum multi-state SWAP test based algorithms, the query complexity for correctly identifying two points are not $epsilon$-neighbours is at least O(n3 / ln n)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In machine learning and particularly in topological data analysis, $\epsilon$-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 $\epsilon$-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 $\epsilon$-neighbours is at least O(n^3 / ln n), showing that this approach, if used directly for $\epsilon$-graph construction, does not bring a computational advantage when compared to a classical approach.

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