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arXiv · 2306.04290

Quantum Distance Calculation for $\epsilon$-Graph Construction

Naomi Mona Chmielewski·Nina Amini·Paulin Jacquot·Joseph Mikael
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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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Naomi Mona Chmielewski, Nina Amini, Paulin Jacquot, Joseph Mikael. 2023-06-07. Quantum Distance Calculation for $\epsilon$-Graph Construction. https://arxiv.org/abs/2306.04290

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