⚛️ high-energy experiments

A comparative study of variational quantum classifiers and classical machine learning for $tW-t\bar{t}$ discrimination at the LHC

This study benchmarks the performance of Variational Quantum Classifiers against classical Boosted Decision Trees and Multi-Layer Perceptrons for discriminating $tW$ signal from $t\bar{t}$ background in LHC Run-2 data, identifying specific analysis regimes where quantum-inspired models offer competitive discrimination capabilities.

Original authors: Rohan Hindocha, Priyanka

Published 2026-10-19

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Rohan Hindocha, Priyanka

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

At the Large Hadron Collider, a massive machine buried beneath the border of France and Switzerland, scientists smash protons together at nearly the speed of light to recreate the conditions of the early universe. Among the trillions of collisions that occur, a rare event involves the creation of a top quark, the heaviest known elementary particle, produced alongside a W boson. This specific combination, known as the tW channel, is a crucial laboratory for testing the Standard Model of physics and searching for new, unknown forces. However, finding this rare signal is like trying to hear a single whisper in a roaring stadium. The top quark produced in this way looks almost identical to a much more common event where a pair of top quarks is created and immediately destroyed. Distinguishing the rare signal from the overwhelming background of these common pairs is one of the most difficult challenges in modern particle physics.

For decades, physicists have relied on powerful classical computer algorithms to sort through this data, using techniques that mimic decision trees or neural networks to spot the subtle differences between the two types of events. Recently, a new tool has emerged from the realm of quantum computing: the variational quantum classifier. This is a hybrid system that uses the strange rules of quantum mechanics, where particles can exist in multiple states at once, to process information. While these quantum computers are still in their infancy and currently too noisy to handle the massive data loads of a real collider, researchers wanted to know if the mathematical logic behind them could offer an advantage over the established classical methods. To test this, a team of physicists from the University of Delhi simulated a realistic scenario using open data from the collider's second run, pitting the new quantum-inspired algorithm against the two best-performing classical models: the boosted decision tree and the multi-layer perceptron.

The researchers focused on two distinct ways the particles can appear after a collision. In the first scenario, the particles decay into electrons and muons, creating a relatively clean signal that is easier to spot but rarer. In the second, more common scenario, the particles decay into jets of other particles, creating a messy, crowded environment that is much harder to analyze. They divided the data into different categories based on how many particles were detected and whether those particles were moving slowly or were "boosted" to extremely high speeds. For each of these categories, they trained the three different computer models to learn the difference between the rare tW signal and the common top-quark pair background. The goal was not just to see which model made the fewest mistakes, but to see which one could maximize the statistical significance of the discovery, essentially finding the sweet spot where the most signal is kept while the most background is thrown away.

The results of this comparison were surprisingly balanced. In the clean, electron-muon channel, all three models performed almost identically. The quantum classifier was just as good as the classical decision trees and neural networks at separating the signal from the background, with no statistical advantage for any single approach. In the more complex, messy hadronic channels, the picture was slightly more nuanced. In the regime where the particles are moving at moderate speeds, the classical neural network and the quantum classifier showed a slight edge over the decision trees, though the difference was small enough that it could be attributed to random statistical variation rather than a fundamental superiority. In the regime where particles are moving at very high speeds, the decision trees appeared to find a sharper peak in significance, but this peak was unstable and fluctuated wildly, making it unreliable. The quantum classifier and the neural network, by contrast, produced smoother, more stable curves that maintained a consistent level of performance.

Ultimately, the study demonstrates that the variational quantum classifier is a viable tool for high-energy physics, capable of matching the performance of the best classical algorithms currently in use. The researchers found that while the quantum model did not dramatically outperform the others in this specific simulation, it did not fall behind either. It successfully navigated the complex, high-dimensional data of particle collisions without losing stability. This suggests that as quantum hardware matures and becomes capable of handling real-world data, these algorithms will not need to reinvent the wheel to be useful; they can step in and perform the same critical sorting tasks as the classical tools, potentially offering new ways to handle the unique correlations in particle data that classical computers struggle to see. For now, the quantum classifier stands as a promising peer to the established methods, ready to be tested further as the technology evolves.

Technical Summary: A Comparative Study of Variational Quantum Classifiers and Classical Machine Learning for tW-t¯t Discrimination at the LHC

Problem Statement
Precise measurements of single top-quark production in the associated $tW$ -channel at the Large Hadron Collider (LHC) are hindered by the dominant top-antitop ( $t\bar{t}$ ) background. The final-state topologies of $tW$ and $t\bar{t}$ processes are highly similar, particularly due to Initial-State Radiation (ISR), Final-State Radiation (FSR), and detector reconstruction effects, making their separation a challenging classification problem. While classical machine learning (ML) algorithms like Boosted Decision Trees (BDTs) and Multi-Layer Perceptrons (MLPs) are standard tools for this task, the emergence of Quantum Machine Learning (QML) has prompted an investigation into whether Variational Quantum Classifiers (VQCs) can offer competitive performance. This study aims to benchmark VQCs against established classical methods for the specific task of distinguishing $tW$ signal events from $t\bar{t}$ background events using CMS Open Data (Run-2, 13 TeV).

Methodology
The study utilizes Monte Carlo simulated events from the CMS Open Data portal. The analysis is divided into three distinct topological regimes:

Dileptonic $e-\mu$ channel: Characterized by two leptons and missing transverse energy. Events are categorized into regions based on jet and $b$ -tag multiplicity (specifically $2j1b$ and $2j2b$ ).
Hadronic Resolved regime: Events where top quarks have lower transverse momentum, resulting in distinct, resolved jets (AK4).
Hadronic Boosted regime: Events with highly boosted top quarks, where decay products merge into large-radius jets (AK8).

Data Preparation and Features:

Signal: $tW$ and $\bar{t}W$ events.
Background: Primarily $t\bar{t}$ , with additional backgrounds ( $W$ +jets, QCD multijets, $t$ -channel single top) suppressed via physics-based selection cuts.
Interference Treatment: The Diagram Removal (DR) scheme is applied to $tW$ samples to avoid double-counting resonant $t\bar{t}$ -like contributions.
Feature Sets: Models are trained on kinematic variables (e.g., $H_T$ , $M_{top}$ , $\Delta R$ , substructure variables like $\tau_{21}$ and soft-drop mass) and the analysis region itself. Features are scaled to the $[0, \pi]$ range to accommodate periodic rotation gates.

Model Architectures:

BDT: Implemented via XGBoost with 50 estimators and a maximum tree depth of 2.
MLP: A PyTorch-based network with four hidden layers (128, 128, 64, 32 neurons) using ReLU activation and L2 regularization.
VQC: Implemented using the PennyLane framework with a PyTorch interface. The architecture employs a "StronglyEntanglingLayers" ansatz. Input features are encoded into qubits via $R_y$ and $R_z$ rotation gates. The circuit includes alternating layers of parameterized rotations and CNOT entangling gates (10 layers for $e-\mu$ and resolved channels). The output is derived from the expectation value of the Pauli-Z operator.
Training: All models use the Adam optimizer, Binary Cross-Entropy loss (weighted by event luminosity), and a 70:30 train-test split. The VQC is simulated using the default.qubit ideal state vector simulator, representing an upper bound on performance without hardware noise.

Key Results
The performance of the three classifiers was evaluated using standard ML metrics (AUC, Separation Power) and physics-motivated metrics (Maximum Significance $Z_{max}$ , Significance Gain, Integrated Significance).

Dileptonic $e-\mu$ Channel: All three models (BDT, MLP, VQC) demonstrated statistically indistinguishable performance. AUC values ranged between 0.61 and 0.69 depending on the region, with no significant advantage for any specific architecture.
Hadronic Boosted Regime: Neural network-based models (MLP and VQC) showed slightly higher AUC and separation power values compared to BDT in the signal-enriched ( $1b$ ) region. In the background-enriched ( $2b$ ) region, VQC exhibited the highest separation power. However, BDT produced very sharp peaks in significance curves that were highly unstable (large bootstrap uncertainties), whereas MLP and VQC provided more stable significance curves. The Integrated Significance remained statistically consistent across all models.
Hadronic Resolved Regime: MLP achieved the highest central values for AUC and separation power in the signal region, though differences with BDT and VQC were within statistical uncertainties. In the background region, BDT showed slightly higher central values, but again, the differences were not statistically significant.

Conclusions and Significance
The paper concludes that for the specific task of $tW$ vs. $t\bar{t}$ discrimination with the selected feature sets and limited statistics, the Variational Quantum Classifier performs comparably to established classical algorithms (BDT and MLP).

Performance Parity: The VQC does not outperform classical methods in a statistically significant manner but successfully achieves performance levels equivalent to standard classifiers.
Stability: In the noisy boosted hadronic channel, the VQC (like the MLP) demonstrated more stable significance curves compared to the BDT, which exhibited unstable, high-significance peaks.
Feasibility: The study establishes that VQCs are a viable tool for High Energy Physics (HEP) background discrimination. The authors suggest that while current results are modest, the unique properties of quantum entanglement and superposition within the VQC architecture could offer advantages in more complex analysis regimes where neural networks already outperform BDTs (e.g., top-tagging or jet reconstruction), provided future studies can leverage larger datasets and potentially noisy intermediate-scale quantum (NISQ) hardware.

The work serves as a systematic benchmark, identifying that quantum-inspired models are competitive with classical techniques in realistic HEP classification tasks, particularly in regimes where neural network architectures are already preferred.

More like this