Hybrid Quantum Processors: Molecular Ensembles as Quantum Memory for Solid State Circuits

We investigate a hybrid quantum circuit where ensembles of cold polar molecules serve as long-lived quantum memories and optical interfaces for solid state quantum processors. The quantum memory realized by collective spin states (ensemble qubit) is coupled to a high-$Q$ stripline cavity via microwave Raman processes. We show that, for convenient trap-surface distances of a few $\mu \mathrm{m}$, strong coupling between the cavity and ensemble qubit can be achieved. We discuss basic quantum information protocols, including a swap from the cavity photon bus to the molecular quantum memory, and a deterministic two qubit gate. Finally, we investigate coherence properties of molecular ensemble quantum bits.

Figure 1

(a) Ensembles of polar molecules and a CPB are coupled via the quantized field of a stripline cavity (see text for more details). (b) Rotational excitation spectrum of molecules with a ${}^2\Sigma _{1/2}$ ground state where we plot excited states according to the Hamiltonian $H=H_R+H_{\mathrm{SR}}$. For nonzero nuclear spin $\overrightarrow{I}$ (here $I=1/2$) the hyperfine interaction leads to an additional splitting ($b\sim 2\pi \times 100\mathrm{MHz}$) into eigenstates of $\overrightarrow{F}=\overrightarrow{J}+\overrightarrow{I}$ (hyperfine splitting for the excite states is not shown). Two qubit states in the $N=0$ manifold, $|0⟩$, $|1⟩$ are coupled by a Raman process involving a single cavity photon and an external microwave field, $\Omega (t)$.

Figure 2

(a) Adiabatic energies levels for the states $|n{⟩}_c|g⟩$ as a function of the charge qubit detuning ${\delta }_c$. (b) Evolution of the dynamical phases ${\varphi }_1$ (solid line) and ${\varphi }_2$ (dashed line) for a pulse ${\delta }_c(t)=-{\delta }_0(2t/T-1{)}^2-{\delta }_1$, ${\delta }_0/g_c=30$, ${\delta }_1/g_c=0.44$, and $T=44.79/g_c$. For the same pulse ${\delta }_c(t)$ the resulting fidelity of the total gate sequence, ${\mathcal{F}}_G$ (averaged over all initial states $|\psi {⟩}_m$), is plotted in (c) for different values of the charge qubit dephasing rate, $T_2^{-1}$, and the cavity loss rate $\kappa$.