Maxwell, J. C. VIII. A dynamical theory of the electromagnetic field. Philos. Trans. R. Soc. Lond. 155, 459–512 (1865).
Maxwell, J. C. A Treatise on Electricity and Magnetism Vol. 1 (Clarendon Press, 1873).
Newton, I. Opticks, or, a Treatise of the Reflections, Refractions, Inflections & Colours of Light (Courier Corporation, 1952).
Young, T. I. The Bakerian lecture. experiments and calculations relative to physical optics. Philos. Trans. R. Soc. Lond. 94, 1–16 (1804).
De Broglie, L. Waves and quanta. Nature 112, 540 (1923).
Azuma, K. et al. Quantum repeaters: from quantum networks to the quantum internet. Rev. Mod. Phys. 95, 045006 (2023).
Wang, W. et al. Quantum-enhanced radiometry via approximate quantum error correction. Nat. Commun. 13, 3214 (2022).
Deng, X. et al. Quantum-enhanced metrology with large fock states. Nat. Phys. 20, 1874 (2024).
McCormick, K. C. et al. Quantum-enhanced sensing of a single-ion mechanical oscillator. Nature 572, 86 (2019).
Liu, Y. et al. Hybrid oscillator-qubit quantum processors: instruction set architectures, abstract machine models, and applications. PRX Quantum 7, 010201 (2026).
Cai, W., Ma, Y., Wang, W., Zou, C.-L. & Sun, L. Bosonic quantum error correction codes in superconducting quantum circuits. Fundam. Res. 1, 50 (2021).
Joshi, A., Noh, K. & Gao, Y. Y. Quantum information processing with bosonic qubits in circuit QED. Quantum Sci. Technol. 6, 033001 (2021).
Wang, C. S. et al. Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor. Phys. Rev. X 10, 021060 (2020).
Yuan, L., Lin, Q., Xiao, M. & Fan, S. Synthetic dimension in photonics. Optica 5, 1396 (2018).
Deng, J. et al. Observing the quantum topology of light. Science 378, 966 (2022).
Braunstein, S. L. & Caves, C. M. Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439 (1994).
Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330 (2004).
Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T. & Glaser, S. J. Optimal control of coupled spin dynamics: design of nmr pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172, 296 (2005).
Heeres, R. W. et al. Implementing a universal gate set on a logical qubit encoded in an oscillator. Nat. Commun. 8, 94 (2017).
Eickbusch, A. et al. Fast universal control of an oscillator with weak dispersive coupling to a qubit. Nat. Phys. 18, 1464 (2022).
Krastanov, S. et al. Universal control of an oscillator with dispersive coupling to a qubit. Phys. Rev. A 92, 040303 (2015).
Heeres, R. W. et al. Cavity state manipulation using photon-number selective phase gates. Phys. Rev. Lett. 115, 137002 (2015).
Fösel, T., Krastanov, S., Marquardt, F. & Jiang, L. Efficient cavity control with snap gates. Preprint at http://arxiv.org/abs/2004.14256 (2020).
Kudra, M. et al. Robust preparation of Wigner-negative states with optimized snap-displacement sequences. PRX Quantum 3, 030301 (2022).
Hofheinz, M. et al. Generation of fock states in a superconducting quantum circuit. Nature 454, 310 (2008).
Wang, H. et al. Measurement of the decay of Fock states in a superconducting quantum circuit. Phys. Rev. Lett. 101, 240401 (2008).
Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546 (2009).
Chu, Y. et al. Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator. Nature 563, 666 (2018).
Premaratne, S. P., Wellstood, F. C. & Palmer, B. S. Microwave photon Fock state generation by stimulated raman adiabatic passage. Nat. Commun. 8, 14148 (2017).
Wang, W. et al. Converting quasiclassical states into arbitrary Fock state superpositions in a superconducting circuit. Phys. Rev. Lett. 118, 223604 (2017).
Lingenfelter, A., Roberts, D. & Clerk, A. A. Unconditional fock state generation using arbitrarily weak photonic nonlinearities. Sci. Adv. 7, eabj1916 (2021).
Bretheau, L., Campagne-Ibarcq, P., Flurin, E., Mallet, F. & Huard, B. Quantum dynamics of an electromagnetic mode that cannot contain N photons. Science 348, 776 (2015).
Kolner, B. H. Space-time duality and the theory of temporal imaging. IEEE J. Quantum Electron. 30, 1951 (1994).
Karpiski, M., Jachura, M., Wright, L. J. & Smith, B. J. Bandwidth manipulation of quantum light by an electro-optic time lens. Nat. Photon. 11, 53 (2017).
Tirole, R. et al. Double-slit time diffraction at optical frequencies. Nat. Phys. 19, 999 (2023).
Peschel, U., Pertsch, T. & Lederer, F. Optical bloch oscillations in waveguide arrays. Opt. Lett. 23, 1701 (1998).
Christodoulides, D. N., Lederer, F. & Silberberg, Y. Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature 424, 817 (2003).
Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162 (2004).
Blais, A., Grimsmo, A. L., Girvin, S. M. & Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 93, 025005 (2021).
Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).
Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515 (2007).
Li, M. et al. Scalable generation of macroscopic Fock states exceeding 10,000 photons. Preprint at https://arxiv.org/abs/2601.05118 (2026).
Chen, H.-T., Taylor, A. J. & Yu, N. A review of metasurfaces: physics and applications. Rep. Prog. Phys. 79, 076401 (2016).
Chen, W. et al. Carving complex many-atom entangled states by single-photon detection. Phys. Rev. Lett. 115, 250502 (2015).
Burger, S. et al. Dark solitons in Bose–Einstein condensates. Phys. Rev. Lett. 83, 5198 (1999).
Denschlag, J. et al. Generating solitons by phase engineering of a Bose–Einstein condensate. Science 287, 97 (2000).
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).