Quantum Log-Determinant Methods for Torsion-Sensitive Topological Data Analysis

arXiv:2609.40216 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Block Encoding — 13× in this paper · explained in 4 episodes
• Benchmark — 10× in this paper · explained in 2 episodes
• Persistent Homology — 8× in this paper · explained in 3 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Trace — 6× in this paper · explained in 2 episodes
• Query Complexity — 4× in this paper · explained in 2 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Spectral Gap — 3× in this paper · explained in 5 episodes
• Adaptive Algorithm — 1× in this paper · explained in 1 episode
• Admissibility — 1× in this paper · explained in 2 episodes
• Approximate Counting — 1× in this paper · explained in 1 episode
• Approximation Bound — 1× in this paper · explained in 1 episode
• Chebyshev Polynomials — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Topological Data Analysis (TDA) — 1× in this paper · explained in 2 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes

Sources

• Complexity of Supersymmetric Systems and the Cohomology Problem
• Quantum machine learning with subspace states
• Towards quantum topological data analysis: torsion detection
• Quantum Topological Data Analysis Beyond Betti Numbers: Complexity Hardness & An Algorithm for Torsion Witness
• Torsion detection in clique complexes is conditionally QMA 1-hard

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