Mio Komuro

Topological data analysis (TDA) extracts global features of data via Betti numbers, but classical computation becomes costly for large simplicial complexes. We propose a scalable quantum TDA algorithm for Betti number estimation based on a block-encoded Dirac operator and logarithmic-depth circuit construction using reconfigurable beam splitter architectures. The method combines shallow Gaussian-Chebyshev spectral filtering with resource-focused complexity analysis. We derive error bounds, estimate gate and qubit requirements, and numerically validate correct Betti number estimation on small instances. Our results indicate that larger instances remain challenging at present but continued progress in quantum hardware may enable increasingly larger problem sizes to become realistic targets in the future.