Quantum Advantage in Topological Data Analysis via Mayer Homology

arXiv:2609.28058 · quant-ph · Submitted 2026-09-23 · Read on arXiv

quant-ph

Submitted: 2026-09-23

Updated: 2026-09-23

Terminology

• Spectral Gap — 16× in this paper · explained in 5 episodes
• Core — 11× in this paper · explained in 2 episodes
• Persistent Homology — 10× in this paper · explained in 3 episodes
• APEX — 6× in this paper · explained in 1 episode
• Trace — 6× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Benchmark — 4× in this paper · explained in 2 episodes
• Sparsity — 4× in this paper · explained in 4 episodes
• Topological Data Analysis (TDA) — 3× in this paper · explained in 2 episodes
• Anyons — 2× in this paper · explained in 2 episodes
• Block Encoding — 2× in this paper · explained in 4 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Approximate Counting — 1× in this paper · explained in 1 episode
• Artificial Intelligence (AI) — 1× in this paper · explained in 2 episodes
• BQP — 1× in this paper · explained in 2 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Initial Data — 1× in this paper · explained in 2 episodes
• Point Clouds — 1× in this paper · explained in 2 episodes
• Query Complexity — 1× in this paper · explained in 2 episodes
• alpha — 1× in this paper · explained in 1 episode

Sources

• Supersymmetry and Quantum Computation
• Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete
• Complexity of Normalized Persistence Problems for Topological Data Analysis and Local Hamiltonians
• Quantum Topological Data Analysis with Linear Depth and Exponential Speedup
• Hybrid quantum-classical framework for Betti number estimation with applications to topological data analysis
• New aspects of quantum topological data analysis: Betti number estimation, and testing and tracking of homology and cohomology classes
• A quantum algorithm for Khovanov homology
• Topological Sequence Analysis of Genomes: Category theory Approaches
• Topological Sequence Analysis of Genomes: Delta Complex approaches
• Random Simplicial Complexes

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