Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

Understand

In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available.

• Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the lab.
• We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state.
• Our protocols use as a primary non-Gaussian resource a single-photon counter.