  Quantum reservoir engineering is a powerful framework for autonomous quantum
state preparation and error correction. However, traditional approaches to
reservoir engineering are hindered by unavoidable coherent leakage out of the
target state, which imposes an inherent trade off between achievable
steady-state state fidelity and stabilization rate. In this work we demonstrate
a protocol that achieves trade off-free Bell state stabilization in a
qutrit-qubit system realized on a circuit-QED platform. We accomplish this by
creating a purely dissipative channel for population transfer into the target
state, mediated by strong parametric interactions coupling the second-excited
state of a superconducting transmon and the engineered bath resonator. Our
scheme achieves a state preparation fidelity of 84% with a stabilization time
constant of 339 ns, leading to the lowest error-time product reported in
solid-state quantum information platforms to date.
