QINNs: Quantum-Informed Neural Networks

TL;DR

Quantum-informed neural networks (QINNs) address the lack of physics-grounded inductive biases in classical deep learning for collider data by injecting quantum information concepts into traditional models. The authors realise this with a 1P1Q encoding of jet constituents and leverage the Quantum Fisher Information Matrix (QFIM) as a basis-independent descriptor of correlations to perform jet tomography. They demonstrate that QFIM-based embeddings—as non-trainable edge features in graphs or as training priors for simple networks—reveal distinct correlation geometries for QCD and hadronic top jets and yield measurable gains in classification performance and training stability. The approach offers an interpretable, scalable path to quantum-informed collider analyses compatible with near-term hardware and large-scale data, bridging quantum geometry with practical deep learning. Overall, QINNs provide a concrete framework for incorporating quantum observables into collider analysis with tangible interpretability and performance benefits.

Abstract

Classical deep neural networks can learn rich multi-particle correlations in collider data, but their inductive biases are rarely anchored in physics structure. We propose quantum-informed neural networks (QINNs), a general framework that brings quantum information concepts and quantum observables into purely classical models. While the framework is broad, in this paper, we study one concrete realisation that encodes each particle as a qubit and uses the Quantum Fisher Information Matrix (QFIM) as a compact, basis-independent summary of particle correlations. Using jet tagging as a case study, QFIMs act as lightweight embeddings in graph neural networks, increasing model expressivity and plasticity. The QFIM reveals distinct patterns for QCD and hadronic top jets that align with physical expectations. Thus, QINNs offer a practical, interpretable, and scalable route to quantum-informed analyses, that is, tomography, of particle collisions, particularly by enhancing well-established deep learning approaches.

Figures (9)

• Figure 1: Circuit used to construct the VQC
• Figure 2: QFIM for the 30-parameter Variational Quantum Classifier circuit, implemented in PennyLanepennylane. Left: QFIM averaged over $10^6$ QCD jets. Right: QFIM averaged over $10^6$ jets arising from a top quark jet. The X and Y axes show the parameters corresponding to the trainable rotations applied to each qubit used in the 1P1Q approach, where each jet constituent particle is represented by its own qubit. The matrix elements represent parameter correlations within the quantum circuit, with diagonal elements indicating individual parameter sensitivities and off-diagonal elements capturing inter-parameter dependencies.
• Figure 3: QFIMs and spatial constituent distributions for representative QCD (left) and top quark decay (right) jets, chosen using appropriate cuts on the n-subjettiness ratio $\tau_3/\tau_2$Thaler:2010tr, from the $p_\mathrm{T}$ bin $(700,750)\,$GeV. Top row: Full $30 \times 30$ QFIMs with values clipped to the range $[-0.4,0.4]$. Bottom row: Spatial distributions of jet constituents in the $\eta$-$\phi$ plane, with lines connecting constituents representing the strength of correlations derived from the reduced QFIM using the Frobenius norm, and the colour of each circle indicating the fraction of jet $p_\mathrm{T}$ carried by that constituent.
• Figure 4: Performance comparison of QFIM-initialised versus randomly initialised NN-based classifiers, with the untrained classifier serving as a baseline.
• Figure 5: Comparison of the randomly initialised and learned final class prototypes for $t\to bq\bar{q'}~$ jets, demonstrating convergence to a structure similar to the mean QFIM. The range of the colour bars is increased so as to account for the unbounded range.