Inverse Design of Phononic Metamaterials Using QAOA-in-QAOA

Phononic metamaterials, such as phononic crystals and vibro-elastic locally resonant metamaterials, offer unique control over wave propagation via non-local interactions, enabling advanced functionalities like negative refraction and enhanced vibration isolation. However, practical applications are limited by challenges in managing complex, large-scale structures and tuning interactions for specific targets. We present a scalable design method using variational quantum algorithms to achieve target dispersion bands in mechanical metamaterials. Our approach applies an inner Quantum Approximate Optimization Algorithm (QAOA) for dispersion band prediction, with an outer QAOA, enhanced by Genetic Programming Symbolic Regression (GPSR), to minimize discrepancies between predicted and target properties. This nested QAOA approach efficiently optimizes geometry and interactions, advancing the design of multifunctional metamaterials.