1 Particle - 1 Qubit: Particle Physics Data Encoding for Quantum Machine Learning

Abstract

We introduce 1P1Q, a novel quantum data encoding scheme for high-energy physics (HEP), where each particle is assigned to an individual qubit, enabling direct representation of collision events without classical compression. We demonstrate the effectiveness of 1P1Q in quantum machine learning (QML) through two applications: a Quantum Autoencoder (QAE) for unsupervised anomaly detection and a Variational Quantum Circuit (VQC) for supervised classification of top quark jets. Our results show that the QAE successfully distinguishes signal jets from background QCD jets, achieving superior performance compared to a classical autoencoder while utilizing significantly fewer trainable parameters. Similarly, the VQC achieves competitive classification performance, approaching state-of-the-art classical models despite its minimal computational complexity. Furthermore, we validate the QAE on real experimental data from the CMS detector, establishing the robustness of quantum algorithms in practical HEP applications. These results demonstrate that 1P1Q provides an effective and scalable quantum encoding strategy, offering new opportunities for applying quantum computing algorithms in collider data analysis.

Figures (6)

• Figure 1: Bloch Sphere: Effect of the input scaling described in Eq. \ref{['eq:scale']} when applied to the ten hardest particles of a QCD and top jet with comparable jet $p_\mathrm{T}$. The value of $w$ converges to a scaling factor $f=7.268$ for the VQC.
• Figure 2: QAE Circuit (left) used for anomaly detection. VQC (right) used for supervised classification. Example circuits with 4 and 8 input particles, respectively.
• Figure 3: Quantum fidelity distributions for a system with $10$ input qubits and a latent space of $2$ qubits.
• Figure 4: AUC scores vs. $\langle 1 - \text{Fidelity} \rangle_{\text{QCD}}$ for different QAE configurations. Models trained on simulated (dashed) and real CMS data (dotted) show consistent trends, with larger input sizes and higher fidelity loss correlating with improved anomaly detection performance.
• Figure 5: Comparison of ROC curves for the VQC and Particle Transformer. The VQC trained on the 1P1Q-encoded dataset closely matches the performance of the state-of-the-art Particle Transformer, despite using significantly fewer trainable parameters, with both being trained on the same number of events and input size of 10 particles.