2 citations · 2 across the 4 of their papers we have counts for
6 papers
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…
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…
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…
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…