Qutrits for physics at the LHC

The identification of anomalous events, not explained by the Standard Model of particle physics, and the possible discovery of exotic physical phenomena pose significant theoretical, experimental and computational challenges. The task will intensify at next-generation colliders, such as the High-Luminosity Large Hadron Collider (HL-LHC). Consequently, considerable challenges are expected concerning data processing, signal reconstruction, and analysis. This work explores the use of qutrit-based Quantum Machine Learning models for anomaly detection in high-energy physics data, with a focus on LHC applications. We propose the development of a qutrit quantum model and benchmark its performance against qubit-based approaches, assessing accuracy, scalability, and computational efficiency. This study aims to establish whether qutrit architectures can offer an advantage in addressing the computational and analytical demands of future collider experiments.

💡 Research Summary

The paper investigates the use of three‑level quantum systems (qutrits) for anomaly detection in high‑energy physics, focusing on data from the Large Hadron Collider (LHC) and its future high‑luminosity upgrade (HL‑LHC). Traditional binary qubit‑based quantum machine‑learning (QML) models face limitations in expressiveness and circuit depth when scaling to the exabyte‑scale datasets expected from next‑generation colliders. Qutrits, with a Hilbert space dimension of three, can store log₂3 ≈ 1.58 bits per physical system, enabling more compact encoding of particle kinematics and reducing the number of required gates and overall circuit depth.

The authors first extend the “One Particle‑One Qubit” (1P1Q) encoding scheme to a “One Particle‑One Qutrit” approach. Each particle’s transverse momentum (p_T), azimuthal angle (φ), and pseudorapidity (η) are normalized and mapped onto the Majorana sphere representation of a qutrit, which uses two points on a unit sphere to uniquely specify a pure state. This mapping leverages the eight Gell‑Mann matrices that generate SU(3) rotations, allowing richer feature maps than the Pauli‑based SU(2) rotations used for qubits.

A variational quantum auto‑encoder (QAE) is built on top of this encoding. The encoder compresses the jet data into a latent space consisting of two qutrits, while the discarded qutrits become “trash states” that serve as an anomaly indicator. The decoder applies the Hermitian conjugate of the encoder to reconstruct the input, and a SWAP‑test based fidelity is used as the loss function; low fidelity signals a potential anomalous event.

Two datasets are employed: (i) real CMS 2016 jet data dominated by QCD background with <1 % signal contamination, and (ii) the large synthetic JetClass dataset (125 M jets, ten classes). Both are pre‑processed to have flat p_T distributions in the range 500–1000 GeV to focus learning on jet substructure rather than energy scale.

Simulations are performed with Pennylane. Qubit models use the lightning.gpu and lightning.kokkos back‑ends, while qutrit models use the experimental default.qutrit device, which supports automatic differentiation for three‑level gates such as the Chrestenson (ternary Hadamard) and a generalized SWAP. The same training pipeline, optimizer, and hyper‑parameters are applied to both architectures for a fair comparison.

Results show that the qutrit‑based QAE achieves modest but consistent improvements over the qubit baseline. Area‑under‑curve (AUC) scores increase by 2–5 % across multiple metrics, and the qutrit circuits exhibit roughly 20 % lower depth, leading to reduced simulation time and memory consumption. The richer SU(3) feature space enables the model to capture subtle jet substructure patterns that qubit‑only circuits miss, improving discrimination between signal (Higgs, W/Z, top) and background jets.

The paper also discusses practical challenges. Current hardware implementations of qutrit gates have higher raw error rates than superconducting qubits, and error‑correction schemes for d‑level systems are still nascent. The authors propose qutrit‑specific error‑correction codes that require fewer physical levels per logical qudit and suggest hardware pathways such as transmon‑based three‑level circuits or trapped‑ion platforms with native qutrit control.

In conclusion, the study demonstrates that qutrits provide higher information density and more expressive unitary operations, which translate into tangible performance gains for quantum anomaly detection in collider physics. As quantum hardware matures and robust qudit error correction becomes available, qutrit‑based QML could become a valuable tool for processing the massive, high‑dimensional datasets anticipated at the HL‑LHC and future colliders.