Many protocols for quantum computation require a quantum memory element to store qubits. We discuss the accuracy with which quantum states prepared in a Josephson junction qubit can be stored in a nanoelectromechanical resonator and then transfered back to the junction. We find that the fidelity of the memory operation depends on both the junction-resonator coupling strength and the location of the state on the Bloch sphere. Although we specifically focus on a large-area, current-biased

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... on junction phase qubit coupled to the dilatational mode of a piezoelectric nanoelectromechanical disk resonator, many our results will apply to other qubit-oscillator models.