Impact of Circuit Depth versus Qubit Count on Variational Quantum Classifiers for Higgs Boson Signal Detection

TL;DR

This work evaluates depth versus width for Variational Quantum Classifiers applied to Higgs boson signal detection using the ATLAS Higgs Challenge 2014 data. Employing PCA to compress 30 features to 4 or 8 latent dimensions, it compares a shallow 4-qubit circuit, a deeper 4-qubit circuit, and an 8-qubit circuit, finding that circuit depth, not width, drives performance on current NISQ hardware. The 4-qubit deep configuration achieves 56.2% accuracy, while 8 qubits degrade to 50.6% due to barren plateaus, illustrating trainability limits in larger Hilbert spaces. The authors propose a 'Squeeze and Deepen' guideline for QML in high-energy physics, emphasizing deeper entangled circuits on compact representations and discussing hardware/topology implications and future enhancements such as QEM and gradient-free optimization. Overall, the study provides a practical architectural roadmap for quantum anomaly detection in HEP under NISQ constraints.

Abstract

High-Energy Physics (HEP) experiments, such as those at the Large Hadron Collider (LHC), generate massive datasets that challenge classical computational limits. Quantum Machine Learning (QML) offers a potential advantage in processing high-dimensional data; however, finding the optimal architecture for current Noisy Intermediate-Scale Quantum (NISQ) devices remains an open challenge. This study investigates the performance of Variational Quantum Classifiers (VQC) in detecting Higgs Boson signals using the ATLAS Higgs Boson Machine Learning Challenge 2014 experiment dataset. We implemented a dimensionality reduction pipeline using Principal Component Analysis (PCA) to map 30 physical features into 4-qubit and 8-qubit latent spaces. We benchmarked three configurations: (A) a shallow 4-qubit circuit, (B) a deep 4-qubit circuit with increased entanglement layers, and (C) an expanded 8-qubit circuit. Experimental results demonstrate that increasing circuit depth significantly improves performance, yielding the highest accuracy of 56.2% (Configuration B), compared to a baseline of 51.9%. Conversely, simply scaling to 8 qubits resulted in a performance degradation to 50.6% due to optimization challenges associated with Barren Plateaus in the larger Hilbert space. These findings suggest that for near-term quantum hardware, prioritizing circuit depth and entanglement capability is more critical than increasing qubit count for effective anomaly detection in HEP data.

Figures (5)

• Figure 1: High-level schematic of the Variational Quantum Circuit (VQC) architecture. The circuit is composed of a ZZFeatureMap for data encoding and a RealAmplitudes ansatz for the trainable variational layers.
• Figure 2: PCA Projection of classification results for the optimal 4-qubit deep circuit (Stage II). The plot illustrates the decision boundary with an accuracy of 56.2%. Black circles indicate misclassified events, showing that the model successfully captures the core cluster of Signal events (Red) against the Background (Blue).
• Figure 3: Confusion Matrix for the 8-qubit configuration (Stage III). The uniform distribution of True Positives and False Positives (Accuracy 50.6%) indicates that the optimizer failed to converge, characteristic of the Barren Plateau phenomenon in higher-dimensional Hilbert spaces.
• Figure 4: Detailed circuit schematic showing the measurement operations used to map the quantum state $|\Psi_{final}\rangle$ to classical binary predictions.
• Figure 5: PCA Projection for the baseline shallow circuit (Stage I). Compared to the deep circuit (Fig. \ref{['fig:deep_result']}), the decision boundary here is significantly less defined, resulting in a lower accuracy of 51.7% and higher misclassification rates.