Quantum computing with a single molecular ensemble and a Cooper-pair box

We propose to encode quantum information in rotational excitations in a molecular ensemble. Using a stripline cavity field for quantum-state transfer between the molecular ensemble and a Cooper-pair-box two-level system, our proposal offers a linear scaling of the number of qubits in our register with the number of rotationally excited states available in the molecules.

Figure 1

(Color online) (a) A Cooper-pair box is strongly coupled to a stripline cavity as realized in [10]. Additionally a cloud of cold polar molecules interacts with the quantized cavity field. (b) Internal level scheme for a single molecule. The reservoir state $\mid 0⟩$ is selectively coupled to each of the excited states $\mid i⟩$ by Raman transitions. (c) Encoding of $K$ qubits in the symmetric states of an ensemble of $N>K$ identical particles.

Figure 2

Left: in order to transfer a molecular state to the cavity we turn on a far-detuned field with ${\delta }_i∕g_i\gg 1$ and sweep through resonance adiabatically following the dressed state $\mid +,0⟩$. To transfer the state back to the molecular ensemble the field is again turned on at ${\delta }_i∕g_i\gg 1$, this time following the $\mid -,0⟩$ state through resonance. Phase errors due to fluctuating $N_0$ (illustrated by the dashed and dotted lines) are exactly canceled, leaving only a geometric phase of $e^{-i\pi }$. Right: when transferring states between the cavity and CPB one must follow the same path back and forth. Hence the geometric phase vanishes. Since there is no fluctuation in the interaction strength $g_c$, the dynamical phase can be tailored to 0 mod $2\pi$.

Figure 3

A conditional phase shift is performed by exploiting that the dressed-state energies are nonlinear in the excitation number $n$. Starting at ${\delta }_{\mathrm{CPB}}\left(0\right)∕g_c\gg 1$ the CPB is tuned close to resonance $\left[{\delta }_{\mathrm{CPB}}\right(T∕2)\sim g_c]$ and back to end at ${\delta }_{\mathrm{CPB}}\left(T\right)∕g_c\gg 1$. The functional form of ${\delta }_{\mathrm{CPB}}\left(t\right)$ is chosen such that ${\phi }_{+,1}=\pi$ mod $2\pi$ while ${\phi }_{\pm ,0}=0$ mod $2\pi$. The dashed line represents the dressed state $\mid -,1⟩$ which at ${\delta }_{\mathrm{CPB}}∕g_c\gg 1$ corresponds to $\mid 2{⟩}_c\mid g{⟩}_{\mathrm{CPB}}$—i.e., a doubly excited state which is not part of the computational Hilbert space.