Training the parametric interactions in an analog bosonic quantum neural network with Fock basis measurement

[2411.19112] Training the parametric interactions in an analog bosonic quantum neural network with Fock basis measurement Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2411.19112 (quant-ph) [Submitted on 28 Nov 2024 ( v1 ), last revised 14 Apr 2026 (this version, v3)] Title: Training the parametric interactions in an analog bosonic quantum neural network with Fock basis measurement Authors: Julien Dudas , Baptiste Carles , Elie Gouzien , Julie Grollier , Danijela Marković View a PDF of the paper titled Training the parametric interactions in an analog bosonic quantum neural network with Fock basis measurement, by Julien Dudas and 4 other authors View PDF HTML (experimental) Abstract: Quantum neural networks promise to extend the power of machine learning into the quantum domain, with potential applications ranging from automatic recognition of quantum states to the control of quantum devices. However, their physical implementation and training remain challenging. In particular, the backpropagation algorithm that underpins the efficiency of classical neural networks cannot generally be applied to large quantum systems, as nonlinear quantum dynamics are not efficiently simulable. Instead, variational quantum circuits typically rely on parameter-shift rules or sampling-based gradient estimation. Here we propose a bosonic quantum neural network based on parametrically coupled Gaussian modes. Although the underlying quantum dynamics are linear, nonlinear output features are generated through Fock-basis measurements. Because Gaussian evolution can be efficiently simulated in the Heisenberg representation, the system admits gradient-based optimization by differentiating a classical model of the dynamics, while the forward evolution itself could be implemented on quantum hardware. This hybrid approach enables end-to-end training of physically meaningful parameters without requiring gradient extraction from the experimental device. Such architectures are naturally compatible with circuit quantum electrodynamics platforms featuring tunable parametric couplers, as well as integrated photonic systems with engineered $\chi$(2) or $\chi$(3) nonlinearities. Our results demonstrate that linear bosonic networks combined with nonlinear measurement provide a scalable and trainable route toward experimentally realizable quantum neural networks. Subjects: Quantum Physics (quant-ph) ; Disordered Systems and Neural Networks (cond-mat.dis-nn) Cite as: arXiv:2411.19112 [quant-ph] (or arXiv:2411.19112v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2411.19112 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Danijela Markovic [ view email ] [v1] Thu, 28 Nov 2024 12:59:19 UTC (462 KB) [v2] Wed, 9 Apr 2025 06:18:22 UTC (806 KB) [v3] Tue, 14 Apr 2026 04:43:30 UTC (1,614 KB) Full-text links: Access Paper: View a PDF of the paper titled Training the parametric interactions in an analog bosonic quantum neural network with Fock basis measurement, by Julien Dudas and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2024-11 Change to browse by: cond-mat cond-mat.dis-nn References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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