UCQM: A Six-Metric Quality Framework for Continuous-Variable Cluster States
Abstract
Continuous-variable (CV) cluster states constitute one of the central resources for measurement-based quantum computation (MBQC). Despite substantial progress in their theoretical development and experimental realization, comparing the quality of different cluster-state topologies remains challenging, as existing approaches typically rely either on qualitative inspection of covariance matrices or on individual metrics that characterize only a single aspect of the underlying correlation structure. In this work, we propose a quantitative evaluation framework that integrates six complementary descriptors of CV cluster states: total correlation strength (SSC), correlation uniformity (CAV), error resilience (EVC), communication overhead (COM), path redundancy (RED), and bottleneck vulnerability (BOT). These quantities are combined into a single \textbf{Unified Cluster Quality Metric (UCQM)}, providing a consistent basis for evaluating and comparing different cluster-state architectures. The proposed framework is applied to four-mode path, square, and star cluster topologies over the squeezing range r ∈ [0.2,1.8]. Across the investigated parameter regime, the square topology consistently achieves the highest UCQM score, indicating the most balanced structural characteristics among the topologies considered and supporting its suitability for measurement-based quantum computation. Because all six metrics are derived directly from covariance-matrix elements together with graph connectivity, the framework naturally extends to arbitrary N-mode cluster states, higher-dimensional lattice geometries, and experimentally reconstructed covariance matrices. Beyond providing a single numerical score, UCQM offers a unified perspective for analyzing the structural quality of CV cluster states and establishes a practical framework for their systematic comparison, optimization, and future design.
Related
- Complexity transition for continuous-variable cluster state
- Exponential advantage in continuous-variable quantum state learning
- Wavelength-shifting attack on a chip-based continuous-variable quantum key distribution system
- High-fidelity WDM/SDM fronthaul system based on state-continuous variable-bit coding and sparse residual enhancement
- Continuous variable payload transmitter for the SPOQC mission
BibTeX
@misc{sarshar2026ucqm,
title = {{UCQM: A Six-Metric Quality Framework for Continuous-Variable Cluster States}},
author = {Saman Sarshar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20852},
eprint = {2609.20852},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20852},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - UCQM: A Six-Metric Quality Framework for Continuous-Variable Cluster States
AU - Saman Sarshar
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20852
UR - https://arxiv.org/abs/2609.20852
AB - Continuous-variable (CV) cluster states constitute one of the central resources for measurement-based quantum computation (MBQC). Despite substantial progress in their theoretical development and experimental realization, comparing the quality of different cluster-state topologies remains challenging, as existing approaches typically rely either on qualitative inspection of covariance matrices or on individual metrics that characterize only a single aspect of the underlying correlation structure. In this work, we propose a quantitative evaluation framework that integrates six complementary descriptors of CV cluster states: total correlation strength (SSC), correlation uniformity (CAV), error resilience (EVC), communication overhead (COM), path redundancy (RED), and bottleneck vulnerability (BOT). These quantities are combined into a single \textbf{Unified Cluster Quality Metric (UCQM)}, providing a consistent basis for evaluating and comparing different cluster-state architectures. The proposed framework is applied to four-mode path, square, and star cluster topologies over the squeezing range r ∈ [0.2,1.8]. Across the investigated parameter regime, the square topology consistently achieves the highest UCQM score, indicating the most balanced structural characteristics among the topologies considered and supporting its suitability for measurement-based quantum computation. Because all six metrics are derived directly from covariance-matrix elements together with graph connectivity, the framework naturally extends to arbitrary N-mode cluster states, higher-dimensional lattice geometries, and experimentally reconstructed covariance matrices. Beyond providing a single numerical score, UCQM offers a unified perspective for analyzing the structural quality of CV cluster states and establishes a practical framework for their systematic comparison, optimization, and future design.
ER -