  We study bifurcation measurement of a multi-level superconducting qubit using
a nonlinear resonator biased in the straddling regime, where the resonator
frequency sits between two qubit transition frequencies. We find that
high-fidelity bifurcation measurements are possible because of the enhanced
qubit-state-dependent pull of the resonator frequency, the behavior of
qubit-induced nonlinearities and the reduced Purcell decay rate of the qubit
that can be realized in this regime. Numerical simulations find up to a
threefold improvement in qubit readout fidelity when operating in, rather than
outside of, the straddling regime. High-fidelity measurements can be obtained
at much smaller qubit-resonator couplings than current typical experimental
realizations, reducing spectral crowding and potentially simplifying the
implementation of multi-qubit devices.
