Barren Plateaus as Destructive Interference: A Diagnostic Framework and Implications for Structured Ansatzes
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Quantum Physics arXiv:2605.01319 (quant-ph) [Submitted on 2 May 2026] Title:Barren Plateaus as Destructive Interference: A Diagnostic Framework and Implications for Structured Ansatzes Authors:Pilsung Kang View a PDF of the paper titled Barren Plateaus as Destructive Interference: A Diagnostic Framework and Implications for Structured Ansatzes, by Pilsung Kang View PDF HTML (experimental) Abstract:Barren plateaus (BPs) are usually described by the exponential suppression of gradient variance, but the mechanism by which gradient signal disappears remains unclear. We show that this phenomenon can be understood as destructive interference among termwise gradient contributions. To make this perspective operational, we introduce a diagnostic framework based on the cancellation ratio $R_k$, the effective term count $N_{\mathrm{eff},k}$, and the interference-quality measure $B_{\mathrm{eff},k}=R_k\sqrt{N_{\mathrm{eff},k}}$. Under a random-sign model, $B_{\mathrm{eff},k}$ remains near a stable baseline, defining a random-sign cancellation regime. For the transverse-field Ising model (TFIM), we find that the hardware-efficient ansatz (HEA) remains close to this regime across system sizes and depths, whereas the Hamiltonian variational ansatz (HVA) systematically escapes it. In particular, HVA exhibits larger $B_{\mathrm{eff},k}$ not merely because $N_{\mathrm{eff},k}$ is larger, but because $R_k$ also remains systematically larger despite the broader term participation. This pattern indicates improved sign organization rather than simple term suppression. We further establish an exact identity that connects the proposed interference diagnostics directly to the standard variance-based theory of BPs. These results position destructive interference as a mechanistic interpretation of BP-like behavior in the regimes studied here, but they do not imply that BPs and destructive interference are universally interchangeable across all architectures and settings. Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG) Cite as: arXiv:2605.01319 [quant-ph] (or arXiv:2605.01319v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.01319 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Pilsung Kang [view email] [v1] Sat, 2 May 2026 08:28:21 UTC (581 KB) Full-text links: Access Paper: View a PDF of the paper titled Barren Plateaus as Destructive Interference: A Diagnostic Framework and Implications for Structured Ansatzes, by Pilsung KangView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cs cs.LG References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)