Low-Cost Fredkin Gate with Auxiliary Space

Effective quantum information processing is tantamount in part to minimization of the quantum resources needed by quantum logic gates. Here, we propose an optimization of an n-controlled-qubit Fredkin gate with a maximum of $2n+1$ two-qubit gates and $2n$ single-qudit gates by exploiting auxiliary Hilbert spaces. The number of logic gates required improves on earlier results on simulating arbitrary n-qubit Fredkin gates. In particular, the optimal result for a one-controlled-qubit Fredkin gate (which requires three qutrit-qubit partial-swap gates) breaks the theoretical nonconstructive lower bound of five two-qubit gates. Furthermore, using an additional spatial-mode degree of freedom, we design a possible architecture to implement a polarization-encoded Fredkin gate with linear optical elements.