Quantum Information Processing with Nanomechanical Qubits

We introduce an approach to quantum information processing where the information is stored in the motional degrees of freedom of nanomechanical devices. The qubits of our approach are formed by the two lowest energy levels of mechanical resonators, which are tuned to be strongly anharmonic by suitable electrostatic fields. Single qubit rotations are conducted by radio-frequency voltage pulses that are applied to individual resonators. Two-qubit entangling gates in turn are implemented via a coupling of two qubits to a common optical resonance of a high finesse cavity. We find that gate fidelities exceeding 99% can be achieved for realistic experimental parameters.

Figure 1

Top row: Illustration of nanomechanical qubits interacting via a common photon mode: (a) The deflection of one resonator locally changes the energy density of the photon field and thus causes a force onto other resonators. (b) By properly tuning the qubit frequencies, noninteracting subsets can be defined. Bottom row: Possible implementation of the device we envision. (c) The mechanical vibration of doubly clamped carbon nanotubes couples optomechanically to the evanescent field of a whispering gallery mode in a high finesse microtoroid. (d) Electrostatic and radio-frequency fields can be applied to each nanotube (black) individually via tip electrodes (blue).

Figure 2

(a) Nonlinear phonon spectrum of a nanobeam in the presence of a softening field $V_0^z$. For $2V_0^z>\hslash {\omega }_{m,0}$, the beam enters the bistable buckling regime. (b) Effective nonlinearity of the phonon spectrum ${\delta }_{21}-{\delta }_{10}$. A sufficiently high value of ${\delta }_{21}-{\delta }_{10}$ suppresses unwanted processes of the type $|11\dots ⟩\to |20\dots ⟩$.

Figure 3

Error $\mathcal{E}=1-F$ of gate operations. Except for the quantities on the horizontal axes, all parameters are as in the setting described in the main text. Solid lines show results for two qubits, and red dots show results for four qubits. Highlighted red dots correspond to the parameter example discussed in the text. (a) Error as a function of the gate time for local and entangling operations. Note that changing the gate time also changes the required coupling rate. (b) Error as a function of the laser detuning. [(c) and (d)] Illustration of the influence of damping for the photons and resonators, respectively.