Universal hybrid three-qubit quantum gates assisted by a nitrogen-vacancy center coupled with a whispering-gallery-mode microresonator

We investigate the construction of two universal three-qubit quantum gates in a hybrid system. The designed system consists of a flying photon and a stationary negatively charged nitrogen-vacancy (NV) center fixed on the periphery of a whispering-gallery-mode (WGM) microresonator, with the WGM cavity coupled to tapered fibers functioning as an add-drop structure. These gate operations are accomplished by encoding the information both on the spin degree of freedom of the electron confined in the NV center and on the polarization and spatial-mode states of the flying photon, respectively. Compared with previous schemes, our proposed scheme leads to a reduction of time and resource consumption in the processing. Moreover, these gates work in a deterministic way with no extra qubits required, which is feasible with current technologies. Both proposed gate operations could be physically implemented in one step, which provides a promising approach for quantum information processing ranging from distributed quantum computation to long-distance quantum communication.

Figure 1

Schematic diagram of the WGM microresonator coupled with two tapered fibers (add-drop structure). (a) Effective energy-level configuration of the NV center. The energy transition from state $|+1\rangle \to |A_2\rangle$ is driven resonantly by the input $s_z=-1$ single photon. The energy transition from state $|-1\rangle \to |A_2\rangle$ will not happen in the present scheme due to large detuning caused by the level splitting. (b) The NV center is fixed on the exterior surface of the WGM microresonator. (c) Input-output relation of the add-drop structure under the bare WGM microresonator.

Figure 2

Schematic diagram for the hybrid Fredkin gate between an electron-spin qubit and two DOFs of the photonic qubit. Here PS denotes a phase shifter that adds a $\pi$ phase shift on the photon when it passes through the device and ${\text{PS}}_1$ denotes another phase shifter that adds a $\pi$ phase shift on the $|L\rangle$ component of the photon relative to the $|R\rangle$ component.

Figure 3

Schematic diagram showing the hybrid Toffoli gate between an electron-spin qubit and two DOFs of a single photon. Here c-PBS represents the polarizing beam splitter that transmits the polarization state $|R\rangle$ and reflects the polarization state $|L\rangle$. The quarter-wave plates (QWP) are used to realize the Hadamard operation on the polarization DOF on the photon: $|R\rangle \to \frac{1}{\sqrt{2}}\left(\right|R\rangle +|L\rangle )$ and $|L\rangle \to \frac{1}{\sqrt{2}}\left(\right|R\rangle -|L\rangle )$. When the propagation direction of the photon is changed, the photon polarization is flipped. Phase flips (PF) are used to flip the polarization state of the photon.

Figure 4

(a) Reflection coefficient $\left|r\right(\omega \left)\right|$ and transmission coefficient $\left|t\right(\omega \left)\right|$ vs the coupling strength $g/\sqrt{\kappa \gamma }$. (b) Fidelities of the gate operations denoted by $F_1$ and $F_2$ vs the coupling strength $g/\sqrt{\kappa \gamma }$. The resonant frequencies are chosen as $w_p=w_c=w_0$.