Introducing the Correlation Concentration Ratio (CCR): Quantitative Framework for Comparing Quantum Cluster States

• URL: http://arxiv.org/abs/2604.23258v1
• Date: Sat, 25 Apr 2026 11:50:43 GMT
• Title: Introducing the Correlation Concentration Ratio (CCR): Quantitative Framework for Comparing Quantum Cluster States
• Abstract summary: The process of generating cluster states with linear, square, and T-shaped topologies has been systematically modeled.<n>The simulation results show that the cluster graph structure is directly reflected in the pattern of quadrature correlations.<n>A metric titled CCR is introduced that quantifies the concentration of effective correlations on the graph edges relative to the total correlations of the system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, numerical simulations of four-mode continuous-variable cluster states with different topologies in the framework of measurement-based quantum computation are presented. By utilizing the symplectic representation and covariance matrix, the process of generating cluster states with linear, square, and T-shaped topologies has been systematically modeled. The simulation results show that the cluster graph structure is directly reflected in the pattern of quadrature correlations; in other words, the theoretical nullifier relations of the cluster states are reproduced in the final covariance matrices. Increasing the squeezing parameter leads to the strengthening of the target correlations and the suppression of unwanted components arising from anti-squeezing; such that the off-diagonal elements of the covariance matrix in the linear and square topologies increase to significant values, and in the T-shaped topology a stronger central correlation (similar to GHZ-like behavior in the continuous-variable domain) is observed. In order to quantitatively analyze these structural differences, a metric titled CCR (Correlation Concentration Ratio) is introduced that quantifies the concentration of effective correlations on the graph edges relative to the total correlations of the system. This index enables direct comparison of different topologies from the perspective of structural entanglement distribution and provides a framework for evaluating the efficiency of cluster graphs in MBQC architectures. The results show that CCR can be used as a practical tool for designing and selecting optimal topologies in larger clusters and more complex structures.

Related papers

• Affinity Graph Connectivity in Convex Clustering [2.788593861900701]
  We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph.<n>These bounds and their analysis lead to a better understanding of clustering behavior under various implied connectivity structures behind the data.
  arXiv  Detail & Related papers  (2026-05-23T17:17:36Z)
• K-Models: a Flexible and Interpretable Method for Ordinal Clustering with Application to Antigen-Antibody Interaction Profiles [65.21921642886367]
  K-Models is a novel framework that integrates ordinal constraints and estimates key underlying elements of the random process generating the observed functional profiles.<n>The proposed method is evaluated through simulations and real-world applications.
  arXiv  Detail & Related papers  (2026-05-14T13:35:44Z)
• A Mean Curvature Approach to Boundary Detection: Geometric Insights for Unsupervised Learning [52.452902154360565]
  We introduce Mean Curvature Boundary Points (MCBP), a novel geometric framework grounded in Geometric Machine Learning.<n>MCBP explicitly models the intrinsic curvature of the data manifold and computes pointwise mean curvature without requiring principled manifold parametrization.<n>Experiments on synthetic and real-world datasets demonstrate that MCBP consistently improves clustering performance.
  arXiv  Detail & Related papers  (2026-05-05T20:19:09Z)
• The Mean-Field Dynamics of Transformers [6.008788032203683]
  By idealizing attention on the sphere, we connect Transformer dynamics to Wasserstein gradient flows (Kuramoto), and mean-shift clustering.<n>Results highlight both the mechanisms that drive representation collapse and the regimes that preserve expressive, multi-cluster structure in deep attention architectures.
  arXiv  Detail & Related papers  (2025-12-01T16:51:00Z)
• Graph Canonical Correlation Analysis [2.588462392029118]
  Canonical correlation analysis (CCA) is a widely used technique for estimating associations between two sets of variables.<n>Recent advancements in CCA methods have expanded their application to decipher the interactions of multiomics datasets.<n>We propose the graph Canonical Correlation Analysis (gCCA) approach, which calculates canonical correlations based on the graph structure of the cross-correlation matrix.
  arXiv  Detail & Related papers  (2025-02-03T19:41:06Z)
• Self-Supervised Graph Embedding Clustering [70.36328717683297]
  K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. We propose a unified framework that integrates manifold learning with K-means, resulting in the self-supervised graph embedding framework.
  arXiv  Detail & Related papers  (2024-09-24T08:59:51Z)
• Spectral Clustering for Directed Graphs via Likelihood Estimation on Stochastic Block Models [22.421702511126373]
  We leverage statistical inference on block models to guide the development of a spectral clustering algorithm for directed graphs.<n>We establish a theoretical upper bound on the misclustering error of its spectral relaxation, and based on this relaxation, introduce a novel, self-adaptive spectral clustering method for directed graphs.
  arXiv  Detail & Related papers  (2024-03-28T15:47:13Z)
• Applications of flow models to the generation of correlated lattice QCD ensembles [69.18453821764075]
  Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables.
  arXiv  Detail & Related papers  (2024-01-19T18:33:52Z)
• Simple and Scalable Algorithms for Cluster-Aware Precision Medicine [0.0]
  We propose a simple and scalable approach to joint clustering and embedding. This novel, cluster-aware embedding approach overcomes the complexity and limitations of current joint embedding and clustering methods. Our approach does not require the user to choose the desired number of clusters, but instead yields interpretable dendrograms of hierarchically clustered embeddings.
  arXiv  Detail & Related papers  (2022-11-29T19:27:26Z)
• Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization [0.0]
  We introduce in this work clustering models based on a total variation (TV) regularization procedure on the cluster membership matrix. We provide a numerical evaluation of all proposed methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionisation imaging measurement.
  arXiv  Detail & Related papers  (2021-04-25T23:40:41Z)
• Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
  Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals. We propose a general graph estimator based on a novel structured fusion regularization. We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
  arXiv  Detail & Related papers  (2021-03-05T04:42:32Z)
• Clustering Ensemble Meets Low-rank Tensor Approximation [50.21581880045667]
  This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. We propose a novel low-rank tensor approximation-based method to solve the problem from a global perspective. Experimental results over 7 benchmark data sets show that the proposed model achieves a breakthrough in clustering performance, compared with 12 state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-12-16T13:01:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.