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Learning Distances with Topological Quantum Computation

### Alessandra Di Pierro

We present a novel approach to computing Hamming distance and its kernelisation by means of Topological Quantum Computation.
This approach is based on the encoding of binary strings into a topological vector space, whose inner product yields a natural Hamming distance kernel on the strings.
Kernelisation forges a link with the field of Machine Learning, particularly in relation to binary classifiers such as the Support Vector Machine (SVM).
This makes our approach of interest to the quantum machine learning community.