Quantum computation with cat qubits

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