Superconducting quantum many-body circuits for quantum simulation and computing

Quantum simulators are attractive as a means to study many-body quantum systems that are not amenable to classical numerical treatment. A versatile framework for quantum simulation is offered by superconducting circuits. In this perspective, we discuss how superconducting circuits allow the engineering of a wide variety of interactions, which, in turn, allows the simulation of a wide variety of model Hamiltonians. In particular, we focus on strong photon-photon interactions mediated by nonlinear elements. This includes on-site, nearest-neighbor, and four-body interactions in lattice models, allowing the implementation of extended Bose-Hubbard models and the toric code. We discuss not only the present state in analog quantum simulation but also future perspectives of superconducting quantum simulation, which open up when concatenating quantum gates in emerging quantum computing platforms.