  These are the lecture notes from the 2019 Les Houches Summer School on
"Quantum Information Machines". After a brief introduction to quantum error
correction and bosonic codes, we focus on the case of cat qubits stabilized by
a nonlinear multi-photon driven dissipation process. We argue that such a
system can be seen as a self-correcting qubit where bit-flip errors are
robustly and exponentially suppressed. Next, we provide some experimental
directions to engineer such a multi-photon driven dissipation process with
superconducting circuits. Finally, we analyze various logical gates that can be
implemented without re-introducing bit-flip errors. This set of bias-preserving
gates pave the way towards a hardware-efficient and fault-tolerant quantum
processor.
