We report on the analysis and design of atomically thin graphene resonant nanoelectromechanical systems (NEMS) that can be engineered to exhibit anharmonicity in the quantum regime. Analysis of graphene two-dimensional (2D) NEMS resonators suggests that with device lateral size scaled down to ∼10–30 nm, restoring force due to the third-order (Duffing) stiffness in graphene NEMS can rise to equal or even exceed the force of linear stiffness, enabling strongly nonlinear NEMS resonators with anharmonic potential energy that produces sufficient deviation from a quantum harmonic spectrum, which is necessary toward realizing NEMS qubits. Furthermore, the calculations provide device design guidelines and scaling of anharmonicity in graphene NEMS to facilitate future fabrication of graphene NEMS qubits with the desired nonlinear dynamical characteristics and performance. The results in this work shall help open possibilities for engineering a new type of qubits based on 2D resonant NEMS, which may offer a much more miniaturized, densely packed, and scalable qubit platform, supplementing today's mainstream technologies such as superconducting and trapped ion qubits.
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