Quantum Algorithm for Jaccard Similarity

TL;DR

This paper presents a quantum algorithm to efficiently compute Jaccard Similarity between binary vectors, including implementation details on IBM quantum hardware, offering potential speedups over classical methods.

Contribution

It introduces two quantum sub-algorithms for calculating the intersection and union counts, enabling quantum estimation of Jaccard Similarity.

Findings

Quantum algorithms successfully estimate intersection and union counts.

Implementation demonstrated on IBM quantum hardware.

Potential for quantum speedup in similarity computations.

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.