Digital-analog quantum learning on Rydberg atom arrays

TL;DR

This work introduces hybrid digital-analog quantum learning circuits for Rydberg-atom arrays, combining single-qubit rotations with global evolution under the Rydberg Hamiltonian in a circuit family with depth $d=2\ell+1$. It evaluates performance on two representative tasks—MNIST digit classification with classical data and anomaly-detection based quantum phase-boundary learning with quantum data—under realistic noise models. The results show that digital-analog (DA) circuits achieve higher gate fidelities and enhanced noise robustness than purely digital circuits, often with shorter effective depths and near-constant performance across a range of hyperparameters guided by Rydberg physics (e.g., $\Delta/\Omega$, $R_b/a$, and $t$). The findings support the viability of digital-analog quantum learning as a practical near-term approach for variational quantum learning experiments on neutral-atom platforms, with implications for scalable QML tasks and phase-tr diagram explorations.

Abstract

We propose hybrid digital-analog learning algorithms on Rydberg atom arrays, combining the potentially practical utility and near-term realizability of quantum learning with the rapidly scaling architectures of neutral atoms. Our construction requires only single-qubit operations in the digital setting and global driving according to the Rydberg Hamiltonian in the analog setting. We perform a comprehensive numerical study of our algorithm on both classical and quantum data, given respectively by handwritten digit classification and unsupervised quantum phase boundary learning. We show in the two representative problems that digital-analog learning is not only feasible in the near term, but also requires shorter circuit depths and is more robust to realistic error models as compared to digital learning schemes. Our results suggest that digital-analog learning opens a promising path towards improved variational quantum learning experiments in the near term.

Figures (22)

• Figure 1: A VQA consists of a variational quantum circuit exchanging parameters with a classical optimization algorithm.
• Figure 2: Visualization of (a) $\mathcal{A}_2^4$ assuming a time-independent Rydberg Hamiltonian $\mathcal{H}$ and (b) $\mathcal{D}_2^4$. Blocks shaded in blue are implemented digitally in the hyperfine ground state manifold, while blocks shaded in red are implemented by analog global driving in the ground-Rydberg two-level system.
• Figure 3: (a) Estimated fidelity of the time evolution gate on $n=8$ qubits across varying $R_b/a$. Errors bars denote the standard deviation across instances of the noisy gates, which increase as the fidelity decreases. Three points of note are $R_b/a = 0.80$ (cross), $R_b/a = 0.87$ (square), and $R_b/a = 0.98$ (triangle). The fidelity for an 8-qubit digital gate is also shown as the dotted horizontal line. Notice that the time evolution gate where $R_b/a = 0.98$ has almost the same fidelity as the digital gate. (b) Estimated gate fidelity, fixed at $R_b/a = 0.87$ for digital-analog circuits, compared across system sizes with that of digital circuits.
• Figure 4: VQA workflow of the quantum digit classification protocol. Blue boxes are classical; pink boxes are quantum.
• Figure 5: Comparison of accuracies over various digital-analog circuit layer depths $\ell$ and quench times $t$ in the classification of 3 versus 8, fixing $R_b/a = 0.87$, $\Delta/\Omega = 0.8$, and $n=8$ qubits. (a): noiseless model training accuracy, (b): noiseless testing accuracy, (c) noisy model testing accuracy.