Optimizing state stabilization and passive error correction using time-varying dissipation

Tunable couplings between high coherence quantum objects and lossy resonators is a promising approach to state stabilization. However; both analytical and numerical analyses of simple continuous implementations of this technique show that the residual error of the state with increasing lifetime T₁ scales as (U / T₁)^1/2, where U is the energy penalty for off-resonant errors generated by the coupling. We propose the addition of a lossy resonator that is itself parametrically coupled to the first (higher coherence) resonator or qubit. Using numerically optimized pulses coupling between the quantum state and the first (higher coherence) resonator, we use the tunable coupling between the first and second resonators to flush out any occupied states from the error correcting mechanism, and report a steady state residual error scaling of about U / T₁, which is optimal given realistic experimental constraints. We demonstrate such improved scaling for the stabilization in both simple single-qubit states, and more complex passive quantum error correction circuits.