Nanomechanical ancilla qubits generator for error correction algorithms in quantum computation

Abstract: We suggest a nanoelectromechanical setup that generates properly entangled ancillary ("ancilla") qubits for error correction algorithms in quantum computing, demonstrated as an encoder for the three-qubit bit flip code. The setup is based on mesoscopic terminal utilizing the AC Josephson effect between voltage biased superconducting electrodes and mechanically vibrating mesoscopic superconducting grain in the regime of the Cooper pair box, controlled by the gate voltage. Required functionality is achieved by specifically tailored time-protocol of operating two external parameters: bias voltage and gate voltage. The superconducting grain is fixed on the free end of a cantilever, performing controlled in-plane mechanical vibrations, generating the nanomechanical coherent states organised in a pair of entangled cat-states in two perpendicular spatial directions. Cooper pair box and nanomechanical coherent states become three entangled qubits in a particular way: quantum information, initially encoded in superposition of the Cooper pair box states, is transduced into quantum superposition of two special 3-qubit entangled states, $\vert \uparrow + \, + \rangle$ and $\vert \downarrow - \, - \rangle$. It constitutes the basic input state for the three-qubit bit flip code, used in quantum computation mainly for error correction, "installed" on a single physical object in which the last two ancilla qubits are generated by the nanoelectromechanical setup.