The stakes are considerable. Theories that extend the Standard Model, such as supersymmetry and the left-right symmetric model, predict the existence of a heavier cousin of the W boson, dubbed the W-prime boson. If such a particle exists, it would be far too short-lived to observe directly, but it would decay promptly into a top quark and a bottom quark. Catching that decay means identifying highly energetic, or boosted, top-quark jets amid an overwhelming background of jets produced by quantum chromodynamics, the theory of the strong interaction. Previous searches, including early work by the D0 Collaboration in 1995 and a 2017 analysis by the CMS Collaboration, have pushed the lower bound on the mass of a right-handed W-prime boson to 2.4 teraelectronvolts at 95 percent confidence, but the hunt continues at the proposed High Luminosity LHC.

The difficulty lies in the geometry of boosted decays. A top quark is unstable and decays into a b-quark and a W-boson, and when the top quark carries enormous transverse momentum, the decay products are squeezed into a narrow angular cone. Physicists visualize this by building a two-dimensional histogram, called a jet image, in which pixel intensities represent the energy fractions of the detected particles. In a boosted top decay, the subjets from the b-quark and the W decay products can overlap so completely that the resulting image looks strikingly similar to a background QCD jet. Classical convolutional neural networks can achieve accuracies between 90 and 94 percent on such tasks, but the benchmark studies show this often comes at the price of trainable parameter counts ranging from one thousand to 1.46 million, as in the state-of-the-art ResNeXt architecture, with the associated computational cost and overfitting risks.

The new work, led by Hala Elhag of the Deutsches Elektronen-Synchrotron and Humboldt-Universität zu Berlin, together with colleagues at institutions including Northeastern University, the Cyprus Institute, the University of Tokyo and the Physikalisch-Technische Bundesanstalt, tackles this bottleneck with a quantum convolutional neural network, or QCNN. First introduced by Cong, Choi and Lukin in 2019, the QCNN replaces the classical filters and pooling operations of a conventional CNN with parametrized quantum circuits. Because it relies on shallow circuits, the architecture is naturally suited to today’s noisy intermediate-scale quantum devices, and theoretical work has shown that its shallow depth also protects it from the barren plateau problem that cripples the trainability of many deeper quantum models.

Before any quantum processing can happen, the classical jet images must be encoded into quantum states, and the choice of encoding turns out to matter enormously. The team tested four schemes: tensor product encoding, also known as angle encoding; one- and two-layer versions of a hardware-efficient encoding; and a classically hard embedding. Each encoded state is then passed through alternating convolutional and pooling layers built from two-qubit unitary gates. The researchers compared two convolutional circuits, the SO(4) circuit, which performs real-valued transformations with six trainable parameters per two-qubit block, and the more general SU(4) circuit, a universal two-qubit gate set with fifteen trainable parameters. The layers repeat until only a single qubit remains, whose Pauli-Z expectation value serves as the network’s prediction.

The dataset came from the JetNet library, a Python package built on PyTorch that provides open Monte Carlo datasets for machine learning in high-energy physics. The researchers used the TopTagging dataset, containing hadronic top jets as signal and QCD jets as background. Each jet’s particles carry four-momentum components, and the team preprocessed the data using a Lorentz boost fixed at a gamma factor of ten, followed by a Gram-Schmidt orthonormalization that constructs the image coordinates from the three highest-momentum constituents. This transformation makes jet images look similar regardless of the original top-quark boost, easing the learning problem. Principal component analysis then compressed the 28-by-28 pixel images down to just four pixels, preserving 50.54 percent of the dataset’s variance, so that each pixel could be loaded onto a single qubit.

Running everything on a noiseless classical simulator using the PennyLane framework, with the classical CNNs built in TensorFlow, the team varied the loss function, encoding and batch size while carefully matching parameter counts between quantum and classical models. The SO(4) QCNN with 30 parameters faced a CNN with 33; the SU(4) QCNN with 48 parameters faced a CNN with 51. Across 50 averaged training runs of 30 epochs each, the quantum model outperformed its classical counterpart in most configurations, particularly with the SO(4) circuit, the simpler one-layer hardware-efficient encoding, and small batch sizes. Accuracy declined as batch size grew from 16 to 128, and the QCNNs also converged faster in the early epochs. The researchers attribute the poor showing of the more complex encodings to dataset-induced barren plateaus, a trainability pathology linked to data encoding complexity.

The most striking result came from dimensional expressivity analysis, a technique that identifies redundant parameters in a parametric quantum circuit by checking whether the derivative of the circuit’s output with respect to each parameter can be written as a linear combination of the others. Applying this analysis to the SU(4) circuit revealed that 17 of its 48 parameters were redundant, leaving a minimal, maximally expressive circuit of just 31 parameters. Trained with mean-square-error loss and the one-layer hardware-efficient encoding over 1000 runs, this trimmed quantum circuit achieved higher accuracy than a comparable 33-parameter CNN. When the classical side was beefed up with additional dense layers, pushing the CNN to 73 and then 91 parameters, the 31-parameter quantum circuit still beat the 73-parameter model and matched the performance of the largest classical network.

The authors are careful about what these results do and do not prove. Because everything ran on a noiseless simulator, the effects of hardware noise, finite-shot sampling and circuit depth remain untested, and they explicitly caution that the findings should not be read as a demonstration of practical quantum advantage. They also note that QCNNs processing classical data have been shown to be effectively classically simulable, which paradoxically is an asset: it allows researchers to scale up simulations to many more qubits and work directly with full-resolution jet images, bypassing the lossy PCA step. Accuracy comparisons with other published top-taggers are likewise not straightforward, since results depend heavily on dataset and preprocessing choices, and real experiments must classify single jets rather than composite images.

Even with those caveats, the study points to a concrete path forward. Reducing parameter counts matters enormously for eventual deployment on noisy quantum hardware, where every additional gate invites error, and the expressivity-optimized circuit shows that leaner quantum models need not sacrifice accuracy. The team also highlights equivariant quantum neural networks, which build the rotational symmetries of the data directly into the architecture, as a natural next step. And beyond classical jet images, quantum machine learning may eventually prove most powerful on genuinely quantum data, such as the spin entanglement among final-state particles that the ATLAS Collaboration recently observed with top quarks. For now, the message is that in the demanding arena of particle physics classification, carefully designed quantum circuits are already competitive, and the design principles that get them there may matter more than raw qubit counts.

Subject of Research: Quantum convolutional neural networks for top-quark jet image classification in high-energy physics

Article Title: Quantum convolutional neural networks for jet images classification

Article References: Elhag, H., Hartung, T., Jansen, K., Nagano, L., Pirina, G., & Di Tucci, A. (2026). Quantum convolutional neural networks for jet images classification. Quantum Machine Intelligence, 8(2), Article 109. https://doi.org/10.1007/s42484-026-00457-7

Image Credits: AI Generated

DOI: 10.1007/s42484-026-00457-7

Keywords: quantum machine learning, quantum convolutional neural networks, top-quark tagging, jet images, high-energy physics, Large Hadron Collider, dimensional expressivity analysis, principal component analysis, data encoding, barren plateaus, beyond the Standard Model, classical simulation