⚛️ quantum physics

Quantum convolutional neural networks for jet images classification

This paper demonstrates that quantum convolutional neural networks (QCNNs), particularly when optimized via dimensional expressivity analysis to reduce parameter counts, can outperform classical CNNs in classifying top-quark jet images within a noiseless simulation environment.

Original authors: Hala Elhag, Tobias Hartung, Karl Jansen, Lento Nagano, Giorgio Menicagli Pirina, Alice Di Tucci

Published 2026-10-07

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CC BY 4.0

Original authors: Hala Elhag, Tobias Hartung, Karl Jansen, Lento Nagano, Giorgio Menicagli Pirina, Alice Di Tucci

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the high-energy physics laboratories of the world, scientists smash particles together at nearly the speed of light to uncover the fundamental building blocks of the universe. When these collisions occur, they produce sprays of new particles that fly out in cones, known as jets. To understand what happened in the split second of the crash, physicists must sort through these jets, distinguishing between those created by common background processes and those that might signal the existence of a rare, heavy particle like the top quark. This task is often visualized as a two-dimensional image, where the brightness of each spot represents the energy of a particle hitting the detector. For decades, researchers have used powerful classical computer programs, specifically a type of artificial intelligence called a convolutional neural network, to analyze these images. These programs are excellent at spotting patterns, but as the images become more complex and the particles more energetic, the classical models require massive amounts of computing power and millions of adjustable settings to maintain their accuracy.

A team of researchers has now explored whether the emerging field of quantum computing could offer a more efficient way to solve this specific problem. They turned their attention to a quantum version of the image-analyzing network, known as a quantum convolutional neural network. Instead of using standard computer bits, this system uses quantum bits, which can exist in multiple states at once, to process information. The researchers took a dataset of jet images, which had been simplified to a small grid of pixels, and fed them into both a classical network and several versions of the quantum network. They tested different ways of translating the image data into the quantum system, tried various mathematical methods to measure how well the models were learning, and adjusted the size of the groups of images the models studied at one time. Crucially, they also used a technique to strip away unnecessary parts of the quantum circuit, ensuring that every setting in the machine was doing something useful.

The results of these simulations were promising. In the controlled environment of a noiseless computer simulation, the quantum networks often outperformed their classical counterparts, particularly when using specific configurations like the SO(4) circuit, though performance was similar or slightly worse in other setups like SU(4). While the classical model required a larger number of parameters to reach a similar level of accuracy in these specific tests, the quantum models achieved high precision with a leaner structure. The researchers found that the best performance came from specific ways of encoding the data and using a particular type of quantum gate arrangement. When they applied a method to remove redundant settings from the quantum circuit, the model became even more efficient, retaining its high accuracy while using a comparable number of parameters to the classical model needed to do the same job.

It is important to note that these findings come from simulations run on classical computers that mimic quantum behavior, rather than from experiments on actual quantum hardware. The authors emphasize that real-world quantum computers currently suffer from noise and errors that could disrupt these delicate calculations. Furthermore, while the study compared the quantum model against a classical model with a relatively small number of parameters, the paper notes that the usual case for training classical CNN models in this field involves millions of parameters. However, the study suggests that if these quantum machines can be stabilized, the architecture used here could provide a powerful tool for particle physics. By proving that a quantum network can classify complex jet images with fewer settings than a comparable classical model in this specific context, the work points toward a future where quantum computers might handle the massive data challenges of high-energy physics more efficiently than today's supercomputers, potentially revealing new secrets hidden within the debris of particle collisions.

Technical Summary: Quantum Convolutional Neural Networks for Jet Images Classification

Problem Statement
The paper addresses the challenge of classifying high-energy physics (HEP) jet images, specifically distinguishing top-quark jets from Quantum Chromodynamics (QCD) background jets. While classical Convolutional Neural Networks (CNNs) have been effective for top-tagging, they often struggle to achieve high accuracy when dealing with highly energetic, "boosted" top-quark jet images. In these scenarios, the decay products (subjets) overlap significantly, making the images visually similar to QCD jets and increasing the complexity of feature extraction. State-of-the-art classical architectures, such as ResNeXt, can achieve high accuracy (90–94%) but require millions of trainable parameters, leading to high computational costs and potential overfitting. The authors aim to investigate whether Quantum Machine Learning (QML), specifically Quantum Convolutional Neural Networks (QCNNs), can offer a more parameter-efficient alternative that maintains or improves classification accuracy.

Methodology
The study utilizes the JetNet library's TopTagging dataset, which contains hadronic top jets and QCD jets. The methodology involves the following steps:

Data Preprocessing:
- Image Formation: Jet constituents are transformed into 2D images on the $\eta-\phi$ plane. A Gram-Schmidt orthonormalization is applied to the jet constituents to create a boost-invariant coordinate system, ensuring the images are independent of the initial top-quark momentum.
- Dimensionality Reduction: Principal Component Analysis (PCA) is applied to reduce the image resolution from $28 \times 28$ pixels to $2 \times 2$ pixels (4 input features). This allows the use of a minimal quantum circuit (4 qubits) where each qubit represents a pixel value.
- Dataset Split: The dataset is split into 80% for training and 20% for testing.
Model Architectures:
- Classical Baseline (CNN): A standard CNN architecture is constructed with one Conv2d layer, a MaxPooling layer, a Flatten layer, and two Dense layers. The number of trainable parameters is tuned to match the quantum models (e.g., 33 parameters for the SO(4) comparison).
- Quantum Model (QCNN): The QCNN follows a structure of Encoding $\to$ $\to$ Convolution $\to$ $\to$ Pooling $\to$ $\to$ Measurement.
  - Encodings: Four encoding schemes are tested: Tensor Product Embedding (TPE/Angle), Hardware Efficient Embedding (HEE) with 1 and 2 layers, and Classically Hard Embedding (CHE).
  - Convolutional Circuits: Two unitary two-qubit circuits are tested: $SO(4)$ (real transformations, 6 trainable parameters per block) and $SU(4)$ (universal, 15 trainable parameters per block).
  - Pooling: A pooling circuit reduces the system dimensionality by half using CNOT and single-qubit gates.
  - Measurement: The final output is the expectation value of the Pauli-Z operator on the remaining qubit.
Optimization and Analysis:
- Loss Functions: Cross-entropy, Mean-Square-Error (MSE), and Hinge loss functions are evaluated.
- Dimensional Expressivity Analysis (DEA): To optimize the circuit, DEA is applied to the $SU(4)$ QCNN. This technique identifies and removes redundant trainable parameters while preserving the circuit's maximal expressivity (ability to generate relevant physical states).
- Simulation: All quantum models are simulated on a noiseless classical simulator (PennyLane), while classical models use TensorFlow.

Key Contributions and Results
The paper presents a systematic comparison between QCNN and CNN setups under identical conditions (batch sizes, loss functions, and parameter counts):

Performance Superiority in Low-Parameter Regime: Using a noiseless simulator, QCNNs generally outperform their classical CNN counterparts, particularly when the convolutional block has a lower number of parameters. For instance, an $SO(4)$ QCNN with 30 parameters achieved accuracies up to 99.88% (with HEE1 encoding and MSE loss), whereas the comparable CNN (33 parameters) achieved approximately 96.26%.
Encoding and Batch Size Sensitivity:
- Encodings: HEE1 (1-layer Hardware Efficient Embedding) and TPE yielded the best results. More complex encodings (HEE2, CHE) induced trainability issues, likely due to barren plateaus.
- Batch Sizes: Smaller batch sizes (16 and 32) resulted in higher accuracy and faster convergence compared to larger batches (64, 128), where accuracy tended to decrease.
DEA Optimization: Applying DEA to the $SU(4)$ QCNN reduced the parameter count from 48 to 31 by removing redundant gates. The optimized circuit (31 parameters) maintained high accuracy (99.89%), outperforming the CNN with 33 parameters and achieving comparable results to a CNN with 91 parameters.
Complexity vs. Accuracy: While increasing the complexity of the classical model (via an MLP layer) improved its accuracy, the DEA-optimized QCNN with only 31 parameters still surpassed the 73-parameter CNN and matched the 91-parameter CNN.

Significance and Claims
The authors position this work as a "proof of principle" demonstrating that QCNNs can be effectively utilized for HEP analysis tasks like top-tagging.

Parameter Efficiency: The primary significance lies in demonstrating that QCNNs can achieve superior or comparable classification accuracy to classical CNNs with a significantly reduced number of trainable parameters. This suggests a potential path toward more efficient models that are less prone to overfitting and computationally cheaper to train.
DEA Utility: The study validates DEA as a crucial tool for optimizing quantum circuits, allowing for the removal of redundancy without sacrificing expressivity, which is vital for implementation on Noisy Intermediate-Scale Quantum (NISQ) devices.
Modest Claims on Quantum Advantage: The paper explicitly states that these results do not constitute a demonstration of practical quantum advantage. The simulations were noiseless, and the QCNNs for this specific dataset are classically simulable. The authors emphasize that the results evaluate the performance of the proposed quantum model under ideal conditions. They acknowledge that real-world implementation would require addressing hardware noise, finite-shot sampling, and circuit depth constraints.
Future Directions: The authors suggest that the approach could be extended to higher-dimensional images (avoiding PCA) if larger qubit counts are simulated, and that techniques like Equivariant QNNs (EQNN) could further leverage the symmetries in jet data. They also note the potential for applying these models to inherently quantum datasets in HEP.

Technical Summary: Quantum Convolutional Neural Networks for Jet Images Classification

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