based on a dispersive cross-Kerr coupling between a qubit and its readout resonator. The resulting readout can be high-fidelity and QND, but readout times are currently limited to the order of 50 ns due to the dispersive cross-Kerr of magnitude 10 MHz. Here, we present a new readout scheme that uses the quarton coupler to facilitate a large (greater than 250 MHz) cross-Kerr between a transmon qubit and its readout resonator. Full master equation simulations show a 5 ns readout time with greater than 99% readout and QND fidelity. Unlike state-of-the-art dispersive readout, the proposed „quartonic readout“ scheme relies on a transmon with linearized transitions as the readout resonator. Such operational points are found from a detailed theoretical treatment and parameter study of the coupled system. The quartonic readout circuit is also experimentally feasible and preserves the coherence properties of the qubit. Our work reveals a new path for order-of-magnitude improvements of superconducting qubit readout by engineering nonlinear light-matter couplings in parameter regimes unreachable by existing designs.