Reproduce “Quantum Topological Data Encoding” on OpenResearch

About this paper

Adam Wesołowski, Dimitrios Thanos, Daniel Leykam, Lirandë Pira

This work introduces Quantum Topological Data Encoding (QTDE), a framework that generates quantum representations by evolving initial quantum states using combinatorial Laplacians derived from a dataset's simplicial complex. It demonstrates that this topology-driven quantum evolution captures discriminative structural features, yielding improved classification accuracy on random graph tasks compared to classical baselines.

Key insights

• Topology-driven quantum evolution effectively captures higher-order interactions and global structural patterns, leading to quantum representations with enhanced discriminative power over classical methods.
• Both implicit (fidelity kernel) and explicit (survival features) representations capture similar global organization within datasets, suggesting that much information from the evolved quantum state can be extracted with relatively few measurements.
• Tunable polynomial spectral filters implemented via QSVT can further improve classification accuracy by tailoring the quantum representation to highlight specific spectral properties of the combinatorial Laplacian relevant for data separation.

Summary by alphaXiv.