Design Concepts for Hybrid Superconducting-Mechanical Cat Qubits (Part 2)

Dissipatively-stabilized cat qubits provide a resource-efficient approach to quantum error correction due to their intrinsic exponential noise bias suppressing bit-flip errors. In this work, we present a theoretical study of a second candidate design concept for realizing cat qubits based on mechanical storage resonators. Here we consider an all-silicon nanomechanical resonator and parametrically-enhanced electromechanical coupling to connect an acoustic storage mode to a nonlinear superconducting buffer circuit. Our approach relies on precise Hamiltonian engineering to control decoherence pathways in the composite system. We also develop a method for control and measurement that leverages the existing buffer circuit to perform cat-transmon gates. We find that this hybrid electromechanical platform is capable of substantially longer bit and phase coherence compared to purely superconducting implementations while boasting a small chip footprint, presenting a promising route toward compact, scalable, and fault-tolerant quantum processors.