Abstract
We present a novel approach to computing Hamming distance and its kernelisation within Topological Quantum Computation. This approach is based on an 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.
R. Nagarajan—Partially supported by EU ICT COST Action IC1405 “Reversible Computation Extending Horizons of Computing”.
D. Windridge—Supported by EU Horizon 2020 research project No. 731593 “Dream-like simulation abilities for automated cars (DREAMS4CARS)”.
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Notes
- 1.
The distant union of two arbitrary links L and M, denoted by \( L \sqcup M\) is obtained by first moving L and M so that they are separated by a plane, and then taking the union.
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Di Pierro, A., Mengoni, R., Nagarajan, R., Windridge, D. (2017). Hamming Distance Kernelisation via Topological Quantum Computation. In: Martín-Vide, C., Neruda, R., Vega-Rodríguez, M. (eds) Theory and Practice of Natural Computing. TPNC 2017. Lecture Notes in Computer Science(), vol 10687. Springer, Cham. https://doi.org/10.1007/978-3-319-71069-3_21
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