4 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…
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…
Quantum Speedups for Multiproposal MCMC
Chin-Yi Lin, Kuo-Chin Chen, Philippe Lemey +3
Multiproposal Markov chain Monte Carlo (MCMC) algorithms choose from multiple proposals to generate their next chain step in order to sample from challenging target distributions m…
(Quantum) complexity of testing signed graph clusterability
Kuo-Chin Chen, Simon Apers, Min-Hsiu Hsieh
This study examines clusterability testing for a signed graph in the bounded-degree model. Our contributions are two-fold. First, we provide a quantum algorithm with query complexi…