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In a recent remarkable experiment [R. B. Patel et al., Science advances 2,e1501531 (2016)], a 3-qubit quantum Fredkin (i.e., controlled-SWAP) gate wasdemonstrated by using linear optics. Here we propose a simple experimentalscheme by utilizing the dispersive interaction in superconducting quantumcircuit to implement a hybrid Fredkin gate with a superconducting flux qubit asthe control qubit and two separated quantum memories as the target qudits. Thequantum memories considered here are prepared by the superconducting coplanarwaveguide resonators or nitrogen-vacancy center ensembles. In particular, it isshown that this Fredkin gate can be realized using a single-step operation andmore importantly, each target qudit can be in an arbitrary state with arbitrarydegrees of freedom. Furthermore, we show that this experimental scheme has manypotential applications in quantum computation and quantum informationprocessing such as generating arbitrary entangled states (discrete-variablestates or continuous-variable states) of the two memories, measuring thefidelity and the entanglement between the two memories. With state-of-the-artcircuit QED technology, the numerical simulation is performed to demonstratethat two-memory NOON states, entangled coherent states, and entangled catstates can be efficiently synthesized.

One-step implementation of a hybrid Fredkin gate with quantum memories and single superconducting qubit in circuit QED and its applications