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The development of quantum Josephson circuits has created a strong expectation for reliable processing of quantum information. While this progress has already led to various proof-of-principle experiments on small-scale quantum systems, a major scaling step is required towards many-qubit protocols. Fault-tolerant computation with protected logical qubits comes at the expense of a significant overhead in the hardware, while each of the involved physical qubits still needs to satisfy the best achieved properties (coherence times, coupling strengths and tunability). Here, and in the aim of addressing alternative approaches to deal with these obstacles, I overview a series of recent theoretical proposals, and experimental developments following these proposals, to enable a hardware-efficient paradigm for quantum memory protection and universal quantum computation. In this paradigm, quantum information is encoded, protected and manipulated as a Schrödinger cat state of a quantum harmonic oscillator.