Quantum Algorithm for Jaccard Similarity

Abstract

Jaccard Similarity is a very common proximity measurement used to compute the similarity between two asymmetric binary vectors. Jaccard Similarity is the ratio between the 1s (Intersection of two vectors) to 1s (Union of two vectors). This paper introduces a quantum algorithm for finding the Jaccard Similarity 1s, in the Intersection and Union of two binary vectors. There are two sub-algorithms one for each. Measuring the register for respective algorithm gives count of number of 1 s in binary format. Implementation on IBM composer is also included.