Filling cavities to prevent decay: bosonic quantum error correction

Continuous-variable quantum information processing is a field concerned with using one or more harmonic oscillators to protect, manipulate, and transport quantum information. As opposed to building systems out of two-level components (qubits), here the minimal component is the phase space associated with a canonical pair of continuous variables — position and momentum for a mechanical oscillator or quadrature components for an electromagnetic field mode. The large Hilbert space describing this phase space allows one to encode information such that recovery from errors is possible, thereby providing competitive alternatives to encoding into a register of qubits. Moreover, we are at the point of realizing full-fledged protocols utilizing such encodings due to significant advances in microwave cavity, atomic ensemble, and trapped ion control. This presentation overviews continuous-variable quantum error-correcting codes, from theoretical capabilities to experimental realizations.