Quantum amplification and simulation of strong and ultrastrong coupling of light and matter Wei Qin, Anton Frisk Kockum, Carlos Sánchez Muñoz, Adam Miranowicz, Franco Nori This review discusses recent advances in amplifying quantum light-matter interactions and simulating ultrastrong light-matter interactions in cavity and circuit quantum electrodynamics, and cavity optomechanics. The importance of light-matter interactions in various fields of physics is highlighted, including quantum optics, quantum information, and quantum chemistry. Amplification of these interactions can improve device performance and enable the exploration of novel phenomena. Ultrastrong coupling, where the interaction strength is comparable to the bare frequencies of the uncoupled systems, has become a hot research topic. The review provides an overview of various methods for amplifying light-matter interactions, including those based on classical and quantum drives, and discusses the simulation of ultrastrong light-matter interactions in different systems. The importance of quantum simulations is emphasized, as they can help overcome experimental challenges in reaching and controlling the ultrastrong coupling regime. The review also covers various experimental demonstrations of parametrically amplified light-matter interactions in trapped-ion and superconducting-circuit systems, as well as the amplification of Kerr-type light-matter interactions with squeezing. The review concludes with a discussion of the potential applications of quantum simulations in various fields, including quantum information processing, quantum metrology, and quantum computing.Quantum amplification and simulation of strong and ultrastrong coupling of light and matter Wei Qin, Anton Frisk Kockum, Carlos Sánchez Muñoz, Adam Miranowicz, Franco Nori This review discusses recent advances in amplifying quantum light-matter interactions and simulating ultrastrong light-matter interactions in cavity and circuit quantum electrodynamics, and cavity optomechanics. The importance of light-matter interactions in various fields of physics is highlighted, including quantum optics, quantum information, and quantum chemistry. Amplification of these interactions can improve device performance and enable the exploration of novel phenomena. Ultrastrong coupling, where the interaction strength is comparable to the bare frequencies of the uncoupled systems, has become a hot research topic. The review provides an overview of various methods for amplifying light-matter interactions, including those based on classical and quantum drives, and discusses the simulation of ultrastrong light-matter interactions in different systems. The importance of quantum simulations is emphasized, as they can help overcome experimental challenges in reaching and controlling the ultrastrong coupling regime. The review also covers various experimental demonstrations of parametrically amplified light-matter interactions in trapped-ion and superconducting-circuit systems, as well as the amplification of Kerr-type light-matter interactions with squeezing. The review concludes with a discussion of the potential applications of quantum simulations in various fields, including quantum information processing, quantum metrology, and quantum computing.