aiqbench analysis
This paper proposes a compact quantum circuit architecture for spectral clustering that approximates eigenproblems using Rayleigh-Ritz formulations, thereby avoiding the computational bottleneck of partial kernel matrix construction. The study provides rigorous shot complexity analysis and validates the approach through finite-shot simulations on canonical datasets, demonstrating tractable sampling behavior for the clustering objective.
Quantum Spectral Clustering Framework via Compact Circuit Structures
arXiv:2309.04465v3 Announce Type: replace Abstract: Spectral machine learning methods based on spectral graph theory are powerful but scale poorly due to costly eigen-analysis. Although various eigenvector approximation methods have been proposed, the construction of a partial kernel matrix still remains within their frameworks. This work presents compact quantum circuit designs for spectral clustering in which the eigenproblem is approximated via a Rayleigh-Ritz formulation that bypasses kernel matrix construction and whose overall depth is dominated by the data-embedding routine. A rigorous shot complexity analysis is provided, showing that the sampling-based estimation remains tractable for the spectral clustering objective including a penalty term. Simulations on canonical datasets demonstrate reliable optimization behavior with an under-parameterized hardware-efficient ansatz. Finite-shot simulations further confirm the predicted sampling behavior of the penalty estimator, validating the main claims as a proof of concept.
Abstract:Spectral machine learning methods based on spectral graph theory are powerful but scale poorly due to costly eigen-analysis. Although various eigenvector approximation methods have been proposed, the construction of a partial kernel matrix still remains within their frameworks. This work presents compact quantum circuit designs for spectral clustering in which the eigenproblem is approximated via a Rayleigh-Ritz formulation that bypasses kernel matrix construction and whose overall depth is dominated by the data-embedding routine. A rigorous shot complexity analysis is provided, showing that the sampling-based estimation remains tractable for the spectral clustering objective including a penalty term. Simulations on canonical datasets demonstrate reliable optimization behavior with an under-parameterized hardware-efficient ansatz. Finite-shot simulations further confirm the predicted sampling behavior of the penalty estimator, validating the main claims as a proof of concept.
arXiv:2309.04465 [quant-ph]
(or arXiv:2309.04465v3 [quant-ph] for this version)
H. Kim, S. Park, and J.-K. K. Rhee, "Quantum Spectral Clustering Framework via Compact Circuit Structures." Advanced Quantum Technologies 9, no. 10 (2026): e70456
https://doi.org/10.1002/qute.70456 DOI(s) linking to related resources
Full text under the publisher's open licence · 168 words
