Rapid qubit readout dependent on the transmission of a single fluxon

The readout speed of qubits is a major limitation for error correction in quantum information science. We show simulations of a proposed device that gives readout of a fluxonium qubit using a ballistic fluxon with an estimated readout time of less than 1 nanosecond, without the need for an input microwave tone. This contrasts the prevalent readout based on circuit quantum electrodynamics, but is related to previous studies where a fluxon moving in a single long Josephson junction (LJJ) can exhibit a time delay depending on the state of a coupled qubit. Our readout circuit contains two LJJs and a qubit coupled at their interface. We find that the device can exhibit single-shot readout of a qubit -- one qubit state leads to a single dynamical bounce at the interface and fluxon reflection, and the other qubit state leads to a couple of bounces at the interface and fluxon transmission. Dynamics are initially computed with a separate degree of freedom for all Josephson junctions of the circuit. However, a collective coordinate model reduces the dynamics to three degrees of freedom: one for the fluxonium Josephson junction and one for each LJJ. The large mass imbalance in this model allows us to simulate the mixed quantum-classical dynamics, as an approximation for the full quantum dynamics. Calculations give backaction on the qubit at $\leq 0.1\%$.