Speaker
Description
Jet substructure studies at the LHC often rely on observables that do not fully capture all possible correlations between constituents, especially at higher irreducible orders. We present two approaches for modelling this structure, based on information theory and quantum information geometry. Both methods use the Fisher Information Matrix, the first being constructed classically using the statistics of the input variables, and the second from the quantum metric tensor, also referred to as the Quantum Fisher Information (QFI) matrix.
In the first approach, we start from classical correlator observables such as the energy correlator functions (ECFs) and energy-energy correlators (EECs), though the approach is general and can be extended to observables such as Energy Flow Polynomials (EFPs) which form a complete basis. Pairwise Fisher graphs, built from the covariances of these observables, cannot distinguish an irreducible multi-observable radiation pattern from a collection of ordinary pairwise correlations. We then show that these irreducible correlations can be better understood using higher-order extensions of the Fisher Information, namely the Amari-Chentsov tensor at third order, and higher order cumulant tensors thereafter. We establish a Fisher-correlator-hypergraph triality by showing that the same tensor (at arbitrary order) constructed from a jet observable basis can serve as a coefficient in a local Kullback-Leibler (KL) expansion, as a connected cumulant of the correlator observables, and as a signed hyperedge weight linking a hypergraph built from these observables. This relation allows for a physics-informed construction of hypergraphs from measured or simulated jet observables (EECs, ECFs or EFPs), supplies weights for higher-order graph Laplacians, and provides a criterion for the compression of observable bases while retaining irreducible higher-order information. We demonstrate the applications of this relation on a set of simple tasks: jet tagging using a BDT-based classifier, and a low-capacity message-passing graph neural network (GNN). The resulting hypergraph-based approaches are shown to retain higher-order structure better than pairwise graphs, and provide a useful inductive bias for designing machine learning algorithms to learn from jet substructure observables.
In the second approach, we use the QFI matrix as a complementary representation of kinematic input data, to improve jet tagging performance of large machine learning models such as GNNs and transformers. This matrix is extracted from a variational quantum circuit (VQC) trained for the same task, and serves as a representation of the intrinsic geometry of the circuit’s state manifold. This can represent structure that classical feature engineering alone finds difficult to learn. With this construction, we fuse these additional input features into an existing classical architecture, and show that this quantum-informed enhancement of classical-only inputs leads to noticeable improvements in jet tagging performance for both a simple GNN architecture, and the state-of-the-art Particle Transformer (ParT) model. These gains are measured using the AUC score and the background rejection, and remain statistically significant across multiple random seeds. We therefore demonstrate that quantum-geometric information can be extracted from classically simulated quantum circuits and be used to improve the performance of large ML models even in the NISQ era, before fault-tolerant quantum hardware becomes available.