Universal photonic quantum gates assisted by ancilla diamond nitrogen-vacancy centers coupled to resonators

We propose two compact, economic, and scalable schemes for implementing optical controlled-phase-flip and controlled-controlled-phase-flip gates by using the input-output process of a single-sided cavity strongly coupled to a single nitrogen-vacancy-center defect in diamond. Additional photonic qubits, necessary for procedures based on the parity-check measurement or controlled-path and merging gates, are not employed in our schemes. In the controlled-path gate, the paths of the target photon are conditionally controlled by the control photon, and these two paths can be merged back into one by using a merging gate. Only one half-wave plate is employed in our scheme for the controlled-phase-flip gate. Compared with the conventional synthesis procedures for constructing a controlled-controlled-phase-flip gate, the cost of which is two controlled-path gates and two merging gates, or six controlled-not gates, our scheme is more compact and simpler. Our schemes could be performed with a high fidelity and high efficiency with current achievable experimental techniques.

Figure 1

(a) Schematic diagram of a diamond NV center coupling to a resonator. (b) Possible $\Lambda$-type level-energy diagram of an NV center. The transitions $|\pm \rangle \to |A_2\rangle$ are resonantly derived by the right $\left(R\right)$-circularly and left $\left(L\right)$-circularly polarized photons, respectively. $|A_2\rangle =\left(\right|E_{-}\rangle |+\rangle +|E_{+}\rangle |-\rangle )/\sqrt{2}$ serves as an ancillary state.

Figure 2

Compact quantum circuit for implementing an optical cpf gate.

Figure 3

Compact quantum circuit for implementing an optical c${}^2$pf gate. ${\mathrm{PBS}}_i(i=1,\cdots ,6)$ represents a polarizing beam splitter which transmits the $H$-polarized photon and reflects the $V$-polarized photon, respectively. ${\mathrm{HWP}}_i(i=1,\cdots ,4)$, the half-wave plate rotated by ${22.5}^{\circ }$, induces the transformations $|H\rangle \to \left(\right|H\rangle +|V\rangle )/\sqrt{2}$ and $|V\rangle \to \left(\right|H\rangle -|V\rangle )/\sqrt{2}$ on the photon. ${\mathrm{HWP}}_i^{\prime }$ rotated by ${45}^{\circ }$ is used to exchange the polarizations of the photon, i.e., $|H\rangle \leftrightarrow |V\rangle$. ${\mathrm{QWP}}_j(j=1,\cdots ,8)$, a quarter-wave plate, achieves the polarization changes of the single photon, i.e., $|R\rangle \leftrightarrow |H\rangle$ and $|L\rangle \leftrightarrow |V\rangle$.

Figure 4

Fidelities of our cpf [solid (red) line] and c${}^2$pf [dashed-dotted (blue) line] gates vs the parameter $\text{g}/\sqrt{\kappa \gamma }$. Here $\text{g}/\sqrt{\kappa \gamma }\ge 0.5$.

Figure 5

The average efficiencies of the cpf (the solid line, red) and c${}^2$pf (the dashed-dotted line, blue) gates vs the parameter $\text{g}/\sqrt{\kappa \gamma }$. Here $\text{g}/\sqrt{\kappa \gamma }\ge 0.5$.