  The amplitude damping time, $T_1$, has long stood as the major factor
limiting quantum fidelity in superconducting circuits, prompting concerted
efforts in the material science and design of qubits aimed at increasing $T_1$.
In contrast, the dephasing time, $T_{\phi}$, can usually be extended above
$T_1$ (via, e.g., dynamical decoupling), to the point where it does not limit
fidelity. In this article we propose a scheme for overcoming the conventional
$T_1$ limit on fidelity by designing qubits in a way that amplitude damping
errors can be detected and converted into erasure errors. Compared to standard
qubit implementations our scheme improves the performance of fault-tolerant
protocols, as numerically demonstrated by the circuit-noise simulations of the
surface code. We describe two simple qubit implementations with superconducting
circuits and discuss procedures for detecting amplitude damping errors,
performing entangling gates, and extending $T_\phi$. Our results suggest that
engineering efforts should focus on improving $T_\phi$ and the quality of
quantum coherent control, as they effectively become the limiting factor on the
performance of fault-tolerant protocols.
