  Coupling a resonator to a superconducting qubit enables various operations on
the qubit, including dispersive readout and unconditional reset. The speed of
these operations is limited by the external decay rate of the resonator.
However, increasing the decay rate also increases the rate of qubit decay via
the resonator, limiting the qubit lifetime. Here, we demonstrate that the
resonator-mediated qubit decay can be suppressed by utilizing the
distributed-element, multi-mode nature of the resonator. We show that the
suppression exceeds two orders of magnitude over a bandwidth of 600 MHz. We use
this "intrinsic Purcell filter" to demonstrate a 40-ns readout with 99.1%
fidelity and a 100-ns reset with residual excitation of less than 1.7%.
