Learning Distances with Topological Quantum Computation

We present a novel approach to computing Hamming distance and its kernelisation within Topological Quantum Computation. This approach is based on the encoding of two binary strings into a topological Hilbert space, whose inner product yields a natural Hamming distance kernel on the two 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 potential interest to the quantum machine learning community.