Complexity phase transition for continuous-variable cluster state

Quantum Physics [Submitted on 9 Apr 2026] Complexity phase transition for continuous-variable cluster state Byeongseon Go, Hyunseok Jeong, Changhun Oh Continuous-variable (CV) cluster states offer a promising platform for large-scale measurement-based quantum computations (MBQC). However, finite squeezing inevitably introduces Gaussian noise during MBQC. While fault-tolerant MBQC schemes exist in principle, they require the scalable incorporation of non-Gaussian resources, such as GKP states, which remain experimentally challenging. Consequently, a central question at this stage is how finite squeezing fundamentally constrains the intrinsic computational power of CV cluster states themselves. In this work, we address this question by analyzing the classical complexity of measurement-based linear optics (MBLO) implemented with such states, motivated by its near-term feasibility and recent experimental progress. We develop an explicit MBLO framework and examine how the squeezing level governs the complexity of the classical simulation of the resulting output states. Specifically, we identify squeezing-level thresholds that delineate classically tractable and intractable regimes, thereby revealing a squeezing-driven complexity phase transition. These findings advance our understanding of the squeezing resources necessary for meaningful quantum computation in current experimental regimes. Furthermore, they underscore the critical need to either scale the squeezing level or integrate error-correction schemes to achieve reliable, large-scale quantum computation with CV cluster states. Comments: 8 + 32 pages, 3 + 11 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.07804 [quant-ph]   (or arXiv:2604.07804v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.07804 Focus to learn more Submission history From: Byeongseon Go [view email] [v1] Thu, 9 Apr 2026 04:57:17 UTC (2,047 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)