Controlled unknown quantum operations on hybrid systems**Project supported by the National Natural Science Foundation of China (Grant Nos. 61303039 and 61201253), Chunying Fellowship, and Fundamental Research Funds for the Central Universities, China (Grant No. 2682014CX095).

Abstract

Any unknown unitary operations conditioned on a control system can be deterministically performed if ancillary subspaces are available for the target systems [Zhou 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.