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.

• Received 11 June 2020
• Revised 26 October 2020
• Accepted 29 October 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.054057