Principles of optics in Fock space for the scalable manipulation of large quantum states

Nature Physics (2026) Cite this article The principles of wave optics provide elegant and scalable control over classical light in spatial and temporal domains. However, in the quantum regime, engineering Fock states of photons has been largely restricted to only a few photons at a time, hindered by the computational and experimental challenges of large Hilbert spaces. Here we introduce a conceptual framework of wave propagation in the quantum domain by treating the photon number in a microwave resonator as a synthetic dimension. In the large-photon limit, the coupling between adjacent Fock states becomes approximately uniform, allowing us to establish an analogy to light propagation. Using a superconducting cavity, we experimentally demonstrate Fock-space analogues of optical propagation, refraction, lensing, dispersion and interference with up to 180 photons. By mapping intuitive optical concepts onto the domain of high-dimensional quantum state engineering, our work provides an approach to scalable control of large-scale quantum systems with thousands of photons and advanced bosonic information processing.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutThe data for Figs. 1–5 are available via Figshare at https://doi.org/10.6084/m9.figshare.30892724 (ref. 47). Source data are provided with this paper.The code used in this study is available from the corresponding author upon reasonable request.Maxwell, J. C. VIII. A dynamical theory of the electromagnetic field. Philos. Trans. R. 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Science 287, 97 (2000).Article ADS Google Scholar Xu, Y. et al. Principles of optics in the Fock space: scalable manipulation of giant quantum states. figshare https://doi.org/10.6084/m9.figshare.30892724 (2026).Download referencesWe thank the USTC Center for Micro and Nanoscale Research and Fabrication. We also acknowledge the Supercomputing Center of USTC.Luyan Sun discloses support for the research of this work from the Quantum Science and Technology-National Science and Technology Major Project (grant number 2021ZD0300200) and the National Natural Science Foundation of China (grant numbers 12550006, 92365301, 92565301, 12404567 and 92165209). C.-L.Z. discloses support for the research of this work from the Quantum Science and Technology-National Science and Technology Major Project (grant number 2021ZD0300200) and the National Natural Science Foundation of China (grant number 92265210). Z.H. discloses support for the research of this work from the National Natural Science Foundation of China (grant number 12504580). W.W. discloses support for the research of this work from the Quantum Science and Technology-National Science and Technology Major Project (grant number 2024ZD0301500) and the National Natural Science Foundation of China (grant number 12474498). W.C. discloses support for the research of this work from the National Natural Science Foundation of China (grant number 12574539), the Fundamental Research Funds for the Central Universities and USTC Research Funds of the Double First-Class Initiative. H.Y. discloses support for the research of this work from the Quantum Science and Technology-National Science and Technology Major Project (grant number 2021ZD0301800) and the National Natural Science Foundation of China (grant number 92365206). Y.X., Y.Z., Lida Sun, J.Z., H.H., L.X., G.X. and M.L. declare no relevant funding.These authors contributed equally: Yifang Xu, Yilong Zhou, Ziyue Hua.Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, ChinaYifang Xu, Yilong Zhou, Ziyue Hua, Lida Sun, Jie Zhou, Weiting Wang, Hongwei Huang, Lintao Xiao & Luyan SunLaboratory of Quantum Information, University of Science and Technology of China, Hefei, ChinaWeizhou Cai, Ming Li & Chang-Ling ZouBeijing Academy of Quantum Information Sciences, Beijing, ChinaGuangming Xue & Haifeng YuHefei National Laboratory, Hefei, ChinaGuangming Xue, Haifeng Yu, Ming Li, Chang-Ling Zou & Luyan SunSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarC.-L.Z. and M.L. conceived the experiment and provided theoretical support. Y.X. and Y.Z. performed the experiment, analysed the data and carried out the numerical simulations under the supervision of Luyan Sun. Z.H. provided simulation support. Y.Z. developed the FPGA technique. Lida Sun helped to calibrate the system. J.Z., W.W., W.C., H.H. and L.X contributed to the experimental support. W.C. fabricated the three-dimensional cavity. G.X. and H.Y. fabricated the tantalum transmon qubits. Y.X., Y.Z., Z.H., M.L., C.-L.Z. and Luyan Sun wrote the paper with input from all authors. C.-L.Z. and Luyan Sun supervised the project.Correspondence to Ming Li, Chang-Ling Zou or Luyan Sun.The authors declare no competing interests.Nature Physics thanks Benjamin Huard and Jonas Larson for their contribution to the peer review of this work. Peer reviewer reports are available.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Figs. 1–10, Table 1, Sections I–VII and References.Source data for Fig. 1e, main, insets (bottom left) and insets (top right).Source data for Fig. 2c,d,g,h,j,k.Source data for Fig. 3b–d.Source data for Fig. 4b–e.Source data for Fig. 5b,c.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsXu, Y., Zhou, Y., Hua, Z. et al. Principles of optics in Fock space for the scalable manipulation of large quantum states. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03370-9Download citationReceived: 16 December 2025Accepted: 09 June 2026Published: 09 July 2026Version of record: 09 July 2026DOI: https://doi.org/10.1038/s41567-026-03370-9Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative