Concentration-Free Quantum Kernel Learning in the Rydberg Blockade

TL;DR

This paper introduces a quantum kernel method that avoids exponential measurement complexity by leveraging Rydberg blockade dynamics, enabling efficient quantum machine learning on near-term devices.

Contribution

It proposes a novel quantum kernel that circumvents exponential concentration issues using Rydberg blockade dynamics, remaining classically hard to simulate.

Findings

Analytical solution of a toy model demonstrating kernel properties

Numerical simulations showing effective learning on real data

Implementation feasibility on current neutral atom quantum computers

Abstract

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 the 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.