Lie-Equivariant Quantum Graph Neural Networks

TL;DR

A Lorentz-equivariant quantum GNN for quark-gluon jet discrimination and it is shown that its performance is on par with its classical state-of-the-art counterpart LorentzNet, making it a viable alternative to the conventional computing paradigm.

Abstract

Discovering new phenomena at the Large Hadron Collider (LHC) involves the identification of rare signals over conventional backgrounds. Thus binary classification tasks are ubiquitous in analyses of the vast amounts of LHC data. We develop a Lie-Equivariant Quantum Graph Neural Network (Lie-EQGNN), a quantum model that is not only data efficient, but also has symmetry-preserving properties. Since Lorentz group equivariance has been shown to be beneficial for jet tagging, we build a Lorentz-equivariant quantum GNN for quark-gluon jet discrimination and show that its performance is on par with its classical state-of-the-art counterpart LorentzNet, making it a viable alternative to the conventional computing paradigm.

Figures (5)

• Figure 1: The coordinate system (left) used to represent components of the particle momentum $\vec{p}$ (see also Fig. 1 in Cara:2024spj). Schematic representation of a gluon jet (middle) and a quark jet (right). The jet constituents (solid lines) are collimated around the jet axis. (Figure adapted from Fig. 1 in Kansal:2021cqp.)
• Figure 2: The ansatz used in our work, which consists of a unitary angle encoding followed by $L=2$ trainable variational layers, which in turn consist each of entangling and parameterized $RY$ rotations for each qubit.
• Figure 3: Lorentz-Equivariant Quantum Block (LEQB). This block ensures equivariance in the coordinate update function $x_{i}^{l+1}$ and invariance in the scalar update function $h_{i}^{l+1}$.
• Figure 4: Classification accuracies for LieEQGNN with quantum architectures in place of $\phi_e$ (top left), $\phi_x$ (top right), $\phi_h$ (middle left), $\phi_m$ (middle right). The lower left panel shows the result from the model where all four $\phi_e$, $\phi_x$, $\phi_h$ and $\phi_m$ are represented with quantum circuits. The lower right panel is the result from the classical model LorentzNet lorentznet.
• Figure 5: The same as Fig. \ref{['fig:accuracy']}, but showing the training loss (blue dashed line) and the validation loss (orange solid line).