Qutrits for physics at the LHC

TL;DR

The paper tackles the challenge of scalable anomaly detection for HL-LHC-scale data by developing a qutrit-based Quantum Autoencoder (QAE) with Majorana encoding and generalized gates. It systematically compares the qutrit implementation to a qubit baseline, showing that qutrits can achieve comparable or improved fidelity and discrimination for LLP-like jet signals, while enabling more compact state representations. The work highlights the SU(3)/SO(3) structure and Majorana sphere as a natural framework for qutrit manipulation, and demonstrates robust gate constructions and encoding strategies within the PennyLane simulation environment. Overall, the results support the potential of qudit-based approaches to address the data- and compute-intensive demands of future collider experiments, with clear directions for scaling to larger qutrits and broader datasets. The study contributes practical methods for qutrit encoding, gate design, and performance assessment in high-energy physics data analysis.

Abstract

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.

Figures (4)

• Figure 1: (a) Majorana qutrit representation. It is constituted by two points $P_1$ and $P_2$ connected to the centre of the sphere by the lines shown in red and blue, respectively Majorana. (b) Eigenstate $\ket{+1}$. (c) Eigenstate $\ket{0}$. (d) Eigenstate $\ket{-1}$
• Figure 2: QAE circuit diagram for a latent space of one qutrit, along with three trash qutrits, three reference qutrits, and a single ancilla qutrit. The structure called Encoder represents the implementation of the Majorana encoding, followed by the adapted variational layer and ending with the implementation of the SWAP test.
• Figure 3: Fidelity distributions for models with three trash qubits/qutrits and a latent space of one qubit/qutrit. (a) Qubit-based model trained on 2016 CMS data. (b) Qutrit-based model trained on 2016 CMS data with $\phi_1 = \varrho_0$ and $\phi_2 = \varrho_z$; (c) Qutrit-based model trained on JetClass simulated CMS data with $\phi_1 = \tau_{12}$ and $\phi_2 = E$; (d) Qubit-based model trained on JetClass simulated CMS data; (e) Qutrit-based model trained on JetClass simulated CMS data with $\phi_1 = \varrho_0$ and $\phi_2 = \varrho_z$; (f) Qutrit-based model trained on JetClass simulated CMS data with $\phi_1 = \tau_{23}$ and $\phi_2 = E$.
• Figure 4: $\tau_N$ distributions through the 4 classes ("QCD", $W \rightarrow q\bar{q}$, $H \rightarrow b\bar{b}$, and $t \rightarrow bq\bar{q}$: (a) $\tau_1$, (b) $\tau_2$, (c) $\tau_3$, (d) $\tau_4$, (e) $\tau_{12}$, (f) $\tau_{23}$.