Hardware Efficient Quantum Kernels Using Multimode Bulk Acoustic Resonators

The kernel trick is a widely applicable technique in machine learning domains that maps datasets that are difficult to classify into a computationally friendly feature space. As the dimension of the dataset scales, these kernel calculations can quickly become computationally intractable or data inefficient. In this work, we extend prior efforts in quantum kernel design for Kerr nonlinear devices by implementing time-dependent simulations of a Kerr-qubit coupled to acoustic resonators. For experimentally feasible parameters, we demonstrate that the Kerr nonlinearity directly induces non-classical behavior in the multimode system, which we use to define and analyze a quantum-enhanced kernel. Finally, we present a brief scaling characterization that demonstrates the computational intractability of classically simulating the kernel as the number of resonators scales.