| Summary: | Strong nonlinear coupling of superconducting qubits and/or photons is a critical building block for quantum information processing. Because of the perturbative nature of the Josephson nonlinearity, linear coupling is often used in the dispersive regime to approximate nonlinear coupling. However, this dispersive coupling is weak and the underlying linear coupling mixes the local modes, which, for example, distributes unwanted self-Kerr nonlinearity to photon modes. Here, we use the quarton to yield purely nonlinear coupling between two linearly decoupled transmon qubits. The quarton's zero ϕ^{2} potential enables an ultrastrong gigahertz-level cross-Kerr coupling, which is an order of magnitude stronger compared to existing schemes, and the quarton's positive ϕ^{4} potential can cancel the negative self-Kerr nonlinearity of qubits to linearize them into resonators. This ultrastrong cross-Kerr coupling between bare modes of qubit-qubit, qubit-photon, and even photon-photon is ideal for applications such as single microwave photon detection, ultrafast two-qubit gates, and readout.
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