Resources for continuous-variable quantum computation: theory and experimental proposals

Continuous-Variable (CV) quantum computation is emerging as a promising alternative to quantum computation with two-level systems. In this approach, typical observables have a continuous spectrum, such as the real and imaginary part of the quantised electromagnetic field. In this context, specific resources, such as the cubic phase state and correspondingly the cubic phase gate, have been known for decades to be resourceful, i.e. to promote the set of classically efficiently simulatable operations to universal quantum computation. So far, efforts for implementing experimentally these resourceful elements have been undertaken in quantum optics, however it has not been possible yet to achieve them. I will present two proposals inspired by quantum optics for achieving the generation of the cubic phase state as well as the implementation of a cubic phase gate with microwave technology. Availability of these elements opens for the quest of CV-NISQs - small CV quantum processors without quantum error correction, where a limited number of operations - yet beyond the domain of the classical simulatable ones - are at disposal.