Hardware-efficient autonomous quantum error correction

We propose a new method to autonomously correct for errors of a logical qubit induced by energy relaxation. This scheme encodes the logical qubit as a multi-component superposition of coherent states in a harmonic oscillator, more specifically a cavity mode. The sequences of encoding, decoding and correction operations employ the non-linearity provided by a single physical qubit coupled to the cavity. We layout in detail how to implement these operations in a practical system. This proposal directly addresses the task of building a hardware-efficient and technically realizable quantum memory.