Implementing optimized time-varying coupling and dissipation in small logical qubit architectures.

Tunable couplings between high coherence quantum objects and lossy resonators is a promising approach to state stabilization. Using an additional lossy resonator to provide a mechanism for the fast reset of the first resonator, a steady state residual error scaling of about 1 / T₁ can be achieved. While this technique has been demonstrated for a single qubit coupled to a single resonator, this work looks at applying the same resonator reset technique for an idealized three qubit bit flip code and the Very Small Logical Qubit (VSLQ), a promising route to passive error correction in superconducting architectures. Optimal device and signal parameters for the VSLQ are well understood for a numerically optimized, continuous coupling strength, so we explore the effects of using an optimized, time-varying coupling strength between the primary qubits and shadow resonators and report a best possible scaling logical qubit lifetime T_L that scales as T₁², where T₁ is the lifetime for a single primary qubit.