Concentration-Free Quantum Kernel Learning in the Rydberg Blockade

Quantum kernel methods (QKMs) offer an appealing framework for machine learning on near-term quantum computers. However, QKMs generically suffer from exponential concentration, requiring an exponential number of measurements to resolve kernel values, with the exception of trivial (i.e., classically simulable) kernels. Here we propose a QKM that is free of exponential concentration, yet remains hard to simulate classically. Our QKM utilizes the weak ergodicity-breaking many-body dynamics in the Rydberg blockade of coherently driven neutral atom arrays. We demonstrate the fundamental properties of our QKM by analytically solving an approximate toy model of its underpinning quantum dynamics, as well as by extensive numerical simulations on randomly generated datasets. We further show that the proposed kernel exhibits effective learning on real data. The proposed QKM can be implemented in current neutral atom quantum computers. Along the way, we uncover novel physical insights into the thermalization of weak ergodicity-breaking systems through the non-stabilizerness of the underlying Rydberg-blockaded dynamics, which directly governs the classical simulability of the proposed kernel.