2 citations · 2 across the 7 of their papers we have counts for
9 papers
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…
Computational complexity of the homology problem with orientable filtration: MA-completeness
Ryu Hayakawa, Casper Gyurik, Mahtab Yaghubi Rad +1
We show the existence of an MA-complete homology problem for a certain subclass of simplicial complexes. The problem is defined through a new concept of orientability of simplicial…
Computational complexity of Berry phase estimation in topological phases of matter
Ryu Hayakawa, Kazuki Sakamoto, Chusei Kiumi
The Berry phase is a fundamental quantity in the classification of topological phases of matter. In this paper, we present a new quantum algorithm and several complexity-theoretica…
Provable quantum speedups for computing persistence in topological data analysis
Casper Gyurik, Alexander Schmidhuber, Robbie King +2
Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We provide an efficient quan…
Quantum Walks on Simplicial Complexes and Harmonic Homology: Application to Topological Data Analysis with Superpolynomial Speedups
Ryu Hayakawa, Kuo-Chin Chen, Min-Hsiu Hsieh
This work investigates whether quantum walks on simplicial complexes exhibit quantum advantages. We introduce a novel quantum walk that encodes the combinatorial Laplacian, a key o…