  Fast, high-fidelity, and quantum nondemolition (QND) qubit readout is an
essential element of quantum information processing. For superconducting
qubits, state-of-the-art readout is 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.
