Quantum Phase Classification of Rydberg Atom Systems Using Resource-Efficient Variational Quantum Circuits and Classical Shadows

TL;DR

This work tackles the challenge of identifying Z2 vs Z3 quantum order in a 51-atom Rydberg chain using a resource-efficient quantum pipeline that combines classical shadow tomography with a minimal 2-qubit variational circuit. A seven-step data-processing workflow (shadow construction, density-matrix reconstruction, Pauli expectations, and PCA-based feature reduction) feeds into a compact encoding-entangling-ansatz circuit trained with SPSA and hinge loss, achieving perfect accuracy on train, validation, and test splits. The approach delivers a dramatic reduction in measurement overhead via classical shadows ($O(\log N)$ vs $O(4^N)$) and leverages a low-dimensional feature space (4 PCA components) to maintain discriminative power with only 2 parameters and depth 7. This combination yields a high resource-accuracy tradeoff (score $f=0.5986$) and demonstrates a practical route for quantum-enhanced condensed matter analysis on near-term devices, with clear directions for hardware deployment, noise studies, and scaling to richer phase spaces.

Abstract

Quantum phase transitions in Rydberg atom arrays present significant opportunities for studying many-body physics, yet distinguishing between different ordered phases without explicit order parameters remains challenging. We present a resource-efficient quantum machine learning approach combining classical shadow tomography with variational quantum circuits (VQCs) for binary phase classification of Z2 and Z3 ordered phases. Our pipeline processes 500 randomized measurements per 51-atom chain state, reconstructs shadow operators, performs PCA dimensionality reduction (514 features), and encodes features using angle embedding onto a 2-qubit parameterized circuit. The circuit employs RY-RZ angle encoding, strong entanglement via all-to-all CZ gates, and a minimal 2-parameter ansatz achieving depth 7. Training via simultaneous perturbation stochastic approximation (SPSA) with hinge loss converged in 120 iterations. The model achieved 100% test accuracy with perfect precision, recall, and F1 scores, demonstrating that minimal quantum resources suffice for high-accuracy phase classification. This work establishes pathways for quantum-enhanced condensed matter physics on near-term quantum devices.

Figures (3)

• Figure 1: Training convergence showing rapid loss decrease and 100% validation accuracy by epoch 2. Dual-axis visualization reveals SPSA optimization effectiveness and absence of overfitting.
• Figure 2: PCA variance explained showing that four principal components capture 98% of variance in the phase classification task. PC1 and PC2 alone explain 75%, indicating phase information concentrates in low-dimensional subspace.
• Figure 3: Exponential measurement complexity reduction: classical shadows require only 500 measurements for 51 qubits compared to $10^{30}$ for full tomography (log scale). This $\sim10^{27}$-fold reduction is the fundamental advantage enabling practical phase classification.