Low-cost Fredkin gate with auxiliary space

TL;DR

This paper presents an optimized method for implementing n-controlled-qubit Fredkin gates using auxiliary spaces, reducing the number of quantum gates needed and enabling a linear optical implementation.

Contribution

It introduces a new optimized approach for Fredkin gates that minimizes quantum resources and proposes a feasible optical architecture for polarization-encoded gates.

Findings

Reduced the number of two-qubit gates for n-controlled Fredkin gates.

Achieved the theoretical lower bound for one-controlled-qubit Fredkin gate.

Designed a linear optical setup for polarization-encoded Fredkin gates.

Abstract

Effective quantum information processing is tantamount in part to the minimization 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 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.