Controlled unknown quantum operations on hybrid systems

Any unknown unitary operations conditioned on a control system can be deterministically performed if ancillary subspaces are available for the target systemsZhou X Q, et al. 2011 Nat. Commun. 2 413. In this paper, we show that previous optical schemes may be extended to general hybrid systems if unknown operations are provided by optical instruments. Moreover, a probabilistic scheme is proposed when the unknown operation may be performed on the subspaces of ancillary high-dimensional systems. Furthermore, the unknown operations conditioned on the multi-control system may be reduced to the case with a control system using additional linear circuit complexity. The new schemes may be more flexible for different systems or hybrid systems.