Selective pulse implementation of two-qubit gates for spin-$\frac{3}{2}$-based fullerene quantum-information processing

We propose two potentially practical schemes to carry out two-qubit quantum gates on endohedral fullerenes $\mathrm{N}@{\mathrm{C}}_{60}$ or $\mathrm{P}@{\mathrm{C}}_{60}$. The qubits are stored in electronic spin degrees of freedom of the doped atom N or P. By means of the magnetic dipolar coupling between two neighboring fullerenes, the two-qubit controlled-NOT gate and the two-qubit conditional phase gate are performed by selective microwave pulses assisted by the refocusing technique. We will discuss the necessary additional steps for the universality of our proposal. We will also show that our proposal is useful for both quantum gating and the readout of quantum information from the spin-based qubit state.

Figure 1

(a) The spectrum of the eigenenergies of the two fullerene system coupled by the magnetic dipole-dipole interaction, where $\omega ={\omega }_1$ and $\Delta =2{\omega }_2-2{\omega }_1=12.7\mathrm{MHz}$. (⋯) represents the degenerate frequency difference between the nearest-neighbor levels in a row or in a column. (b) The spectrum of transition frequency corresponding to (a), where $a=-3∕2$, $-1∕2$, and $1∕2$. The dashed lines correspond to the shift of the solid counterparts by $\Delta$.

Figure 2

Two neighboring fullerenes $A$ and $B$, radiated simultaneously by two in-plane directed microwaves, coupling spin states $\mid -1∕2⟩$ and $\mid -3∕2⟩$. The two-photon process is for resonant transition between $\mid -1∕2,-1∕2⟩$ and $\mid -3∕2,-3∕2⟩$, where $\mid -1∕2,-3∕2⟩$ and $\mid -3∕2,-1∕2⟩$ are nonpopulated intermediate states due to large detuning and weak radiation coupling.

Figure 3

The implementation time $T=2\pi ∕\tilde{\Omega }$ with respect to ${\delta }_1$ in the implementation of our proposed CPHASE gate, based on Eq. (7). The dotted, dashed, and solid curves correspond to gate fidelity 98% (i.e., ${\Omega }_A∕2={\Omega }_B∕2={\delta }_{\min }∕10$), 95% (i.e., ${\Omega }_A∕2={\Omega }_B∕2={\delta }_{\min }∕7$), and 92% (i.e., ${\Omega }_A∕2={\Omega }_B∕2={\delta }_{\min }∕5$), respectively.