Unitary-gate synthesis for continuous-variable systems
Jaromı́r Fiurášek · Physical Review A · 2003
We investigate the synthesis of continuous-variable two-mode unitary gates in the setting where two modes A and B are coupled by a fixed quadratic Hamiltonian $H.$ The gate synthesis consists of a sequence of evolutions governed by Hamiltonian $H,$ which are interspaced by local phase shifts applied to A and $B.$ We concentrate on protocols that require the minimum number of necessary steps and we show how to implement the beam splitter and the two-mode squeezer in just three steps. Particular attention is paid to Hamiltonian ${x}_{A}{p}_{B}$ that describes the effective off-resonant interaction of light with the collective atomic spin.