  Superconducting qubits are among the most promising platforms for building a
quantum computer. However, individual qubit coherence times are not far past
the scalability threshold for quantum error correction, meaning that millions
of physical devices would be required to construct a useful quantum computer.
Consequently, further increases in coherence time are very desirable. In this
letter, we blueprint a simple circuit consisting of two transmon qubits and two
additional lossy qubits or resonators, which is passively protected against all
single qubit quantum error channels through a combination of continuous driving
and engineered dissipation. Photon losses are rapidly corrected through
two-photon drive fields implemented with driven SQUID couplings, and dephasing
from random potential fluctuations is heavily suppressed by the drive fields
used to implement the multi-qubit Hamiltonian. Comparing our theoretical model
to published noise estimates from recent experiments on flux and transmon
qubits, we find that logical state coherence could be improved by a factor of
forty or more compared to the individual qubit $T_1$ and $T_2$ using this
technique. We thus demonstrate that there is substantial headroom for improving
the coherence of modern superconducting qubits with a fairly modest increase in
device complexity.
