Decoherence-free quantum-information processing using dipole-coupled qubits

We propose a quantum-information processor that consists of decoherence-free logical qubits encoded into arrays of dipole-coupled qubits. High-fidelity single-qubit operations are performed deterministically within a decoherence-free subsystem without leakage via global addressing of bichromatic laser fields. Two-qubit operations are realized locally with four physical qubits, and between separated logical qubits using linear optics. We show how to prepare cluster states using this method. We include all non-nearest-neighbor effects in our calculations, and we assume the qubits are not located in the Dicke limit. Although our proposal is general to any system of dipole-coupled qubits, throughout the paper we use nitrogen-vacancy (NV) centers in diamond as an experimental context for our theoretical results.

Figure 1

Energy-level scheme of three qubits, with ${\Delta }_{\pm }=-{\Delta }_{13}\pm \frac{1}{2}({\Delta }_{13}+\Omega )$, for $\Omega \equiv \sqrt{8{\Delta }_{12}^2+{\Delta }_{13}^2}$. In the Dicke limit [19], $\mid \mathsf{b}⟩\equiv \frac{1}{\sqrt{6}}(-2\mid 001⟩+\mid 010⟩+\mid 100⟩)$ and $\mid \mathsf{c}⟩\equiv \frac{1}{\sqrt{2}}(\mid 010⟩-\mid 100⟩)$. The DFS is labeled $\{{\mid 0⟩}_L,{\mid 1⟩}_L\}$ [4].

Figure 2

(a) Population of the levels $\mathsf{a},\dots ,\mathsf{h}$ for ${\xi }_{12}=0.5$, ${\mathcal{E}}_{\mu }=\gamma$, ${\omega }_{\mu }=\frac{1}{2}({\Delta }_{13}-\Omega )$, and $\alpha =0$. For these parameters, $F=0.988$ and the time taken for the transfer $\mathsf{a}\text{−}\mathsf{b}$: $t_{\pi }=0.987{\gamma }^{-1}$. (b) Number of population inversions possible during time period ${\gamma }_{\mathsf{b}}^{-1}$ versus qubit separation with $F=0.98$ and $\alpha =0$. For the separation proposed in Ref. 23, ${\gamma }_{\mathsf{b}}{t}_{\pi }\approx 5\times {10}^{-7}$.

Figure 3

(a) Population of the levels $\mathsf{a},\dots ,\mathsf{h}$, with ${\xi }_{12}=0.15$, ${\mathcal{E}}_{\mu }=6\gamma$, ${\mathcal{E}}_{\nu }=15\gamma$, ${\omega }_{\delta }=170\gamma$, and $\alpha =\frac{\pi }{2}$. For these parameters, $F=0.986$ and the time taken for the transfer $\mathsf{b}\text{−}\mathsf{c}$: $t_{\pi }=9.271{\gamma }^{-1}$. (b) Number of qubit rotations $\mathsf{b}\text{−}\mathsf{c}$ possible during time period $\frac{1}{2}{({\gamma }_{\mathsf{b}}+{\gamma }_{\mathsf{c}})}^{-1}$ versus qubit separation with $F=0.98$ and $\alpha =\frac{\pi }{2}$.

Figure 4

CPHASE gate detailed in Ref. 27 between atom $A$ and atom $B$. The $\frac{1}{4}$-wave plates are labeled with $\frac{\lambda }{4}$, and the polarization detector with $D$. A left-circularly polarized photon $\mid L⟩$ is input at the left, and the subsequent polarization is measured at $D$.

Figure 5

The decoherence-free qubit is trapped in a one-sided optical cavity. The transition $\mathsf{c}\text{−}\mathsf{g}$ is coupled resonantly to the right circularly polarized mode of the cavity with coupling constant $g$. The cavity photon is either transmitted through the cavity mirror with rate ${\kappa }_c$ or lost with rate ${\kappa }_l$. $b_{\mathit{in}}\left(t\right)$ and $b_{\mathit{out}}\left(t\right)$ denote the input and output field operators, respectively.