2 citations · 2 across the 7 of their papers we have counts for
5 papers · 2 filters
Double Localization for Quantum Gibbs Sampler Gaps: From an Abstract Framework to Finite-Group Models
Ryu Hayakawa, Angus Southwell, Caesnan M. G. Leditto +2
We introduce double localization, a framework for proving spectral gaps of quantum Gibbs samplers through two complementary operations: geometric localization, which selects update…
Chern-number estimation: nearly optimal quantum algorithm and provable quantum speedup
Soichiro Imamura, Shintaro Ae, Kazuki Sakamoto +2
Topological phases of matter are characterized by global properties of quantum states beyond conventional local order parameters. The Chern number is a central invariant in this ch…
Quantum Advantage in Topological Data Analysis via Mayer Homology
Nhat A. Nghiem, Ryan Babbush, Adam Zalcman +4
Prior work has explored quantum algorithms for topological data analysis (TDA), revealing the possibility of exponential quantum speedups in estimating the ratios of Betti numbers…
Unweighted Gapped Clique Homology is -complete
Ryu Hayakawa
Deciding whether the clique complex of a given graph has nontrivial homology in a given dimension, under vertex-product weighting and an inverse-polynomial spectral gap promise on…
Complexity of Normalized Persistence Problems for Topological Data Analysis and Local Hamiltonians
Dominic Lowe, M. S. Kim, Roberto Bondesan +1
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 con…