Abstract
The Wigner function (WF) provides a phase-space representation of quantum states, with its negativity serving as a key indicator of nonclassicality. However, reconstructing WFs experimentally or numerically remains notoriously difficult due to their high dimensionality and intensive measurement requirements. In this work, we employ a ResNet-based deep generative model (DGM) to reconstruct WFs from a few accessible marginal distributions. Synthetic datasets are generated for three representative quantum-optical models—the single-atom Jaynes–Cummings model (JCM), the two-qubit Tavis–Cummings model (TJCM), and the pair-coherent state (PCS). The trained DGM faithfully reproduces characteristic quantum features—interference fringes, negativity, collapse–revival dynamics, and model-specific symmetries—with an average L2 error of below 0.15. These results confirm that deep generative learning can accurately infer joint quasi-distributions from sparse data while retaining physically meaningful correlations. Overall, this framework provides an efficient and scalable approach for quantum-state visualization, potentially complementing traditional quantum-state tomography in cavity and circuit QED systems.
*The authors acknowledge fruitful discussions with Clemens Gneiting and Franco Nori. This work is supported by the National Science and Technology Council, Taiwan, with Grants No. MOST 108-2112-M-006-020-MY2, MOST 109-2112-M-006-012, MOST110-2112-M-006-012, MOST 111-2112-M-006-015-MY3, MOST 111-2112-M-A49-014, NSTC 112-2112-M-A49 019-MY3, NSTC 112-2123-M-006-001, MOST 112-2314-B-006-011, MOST 110-2224-E-007-003, and MOST 109-2222 E-006-005-MY2, partially by the Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at NCKU, and partially by the National Center for Theoretical Sciences, Taiwan.
