Complexity of Normalized Persistence Problems for Topological Data Analysis and Local Hamiltonians
Topological data analysis (TDA) is a machine learning technique that uses topology to extract patterns from data and has shown the potential to exhibit quantum advantage. A key concept in TDA is persistent homology, which measures the robustness of topological information at different lengthscales. In this paper, we introduce and study the problem of normalized persistence, a practically motivated and easily interpretable version of persistent homology that counts the fraction of holes that persist at different lengthscales. We prove that a variant of normalized persistence is $\mathsf{DQC}_1$-hard and contained in $\mathsf{BQP}$, giving evidence of an exponential quantum speedup for TDA ...
| Authors | Dominic Lowe, M. S. Kim, Roberto Bondesan et al. |
|---|---|
| Primary category | quant-ph |
| Published | 3 July 2026 |
| Last updated at source | 29 September 2026 |
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