Proposal for implementing universal superadiabatic geometric quantum gates in nitrogen-vacancy centers

We propose a feasible scheme to implement a universal set of quantum gates based on geometric phases and superadiabatic quantum control. Consolidating the advantages of both strategies, the proposed quantum gates are robust and fast. The diamond nitrogen-vacancy center system is adopted as a typical example to illustrate the scheme. We show that these gates can be realized in a simple two-level configuration by appropriately controlling the amplitude, phase, and frequency of just one microwave field. The gate's robust and fast features are confirmed by comparing the fidelity of the proposed superadiabatic geometric phase (controlled-phase) gate with those of two other kinds of phase (controlled-phase) gates.

Figure 1

Level structure and “orange slice” scheme for SGQGs. (a) Two Zeeman levels $|m_s=0\rangle$ and $|m_s=-1\rangle$ of the NV spin-triplet ground state are encoded as the qubit states $|0\rangle$ and $|1\rangle$. The double-sided red arrow indicates level-selective coupling of microwave fields for geometric manipulation of the qubit. (b) Evolution of the cyclic state $|{\lambda }_{+}\rangle$ starting from point $A$ and driven by the superadiabatic (original) Hamiltonian is represented by the polarized vector ${\mathbf{n}}_{+}$ [dot-dashed black line (solid green line)] and the corresponding effective magnetic field ${\mathbf{B}}_s\left({\mathbf{B}}_0\right)$ [dotted blue line (solid red line)]. (c) The level structure describes the hyperfine interaction of the NV electron spin with the ${}^{13}\mathrm{C}$ nuclear spin ($I=1/2$). The thick double-sided red arrow indicates state-selective coupling of microwave fields for the nontrivial two-qubit gates acting on the computational space spanned by $\left\{\right|0,\downarrow \rangle$, $|1,\downarrow \rangle$, $|0,\uparrow \rangle$, $|1,\uparrow \rangle \}$.

Figure 2

The fidelities $F$ versus the deviations of Rabi frequency $\eta {\mathrm{\Omega }}_{sm}$ and frequency detuning $\epsilon {\mathrm{\Omega }}_{sm\left(nh\right)}$ from the ideal gates. (a) Superadiabatic geometric $U_1$ with operation time $T_{sa}=0.64\mu \text{s}$. (b) Adiabatic geometric $U_1$ with $T_a=10T_{sa}$. (c) Nonadiabatic holonomic $U_1$ with $T_{nh}=T_{sa}$. (d) Superadiabatic geometric $U_{cp}$ with operation time $T_{sa}^{\prime }=0.64\mu \text{s}$. (e) Adiabatic geometric $U_{cp}$ with $T_a^{\prime }=10T_{sa}^{\prime }$. (f) Nonadiabatic holonomic $U_{cp}$ with $T_{nh}^{\prime }=T_{sa}^{\prime }$.