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arxiv: 2604.18613 · v1 · submitted 2026-04-15 · 🪐 quant-ph · hep-ex· physics.ins-det

Recognition: unknown

Lund Plane to Bloch (LP2B) Encoding for Object and Polarization Tagging with Quantum Jet Substructure

Fabrizio Napolitano , Luca Della Penna , Tommaso Tedeschi , Livio Fan\`o
Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:16 UTC · model grok-4.3

classification 🪐 quant-ph hep-exphysics.ins-det
keywords quantum machine learningjet substructureLund planepolarization taggingW boson taggingquantum neural networksNISQ hardwarehierarchical networks
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The pith

A new encoding maps jet kinematics from the Lund plane into qubit states, letting a quantum network match large classical models on tagging tasks while using three orders of magnitude fewer parameters.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the Lund Plane to Bloch encoding to convert a clean, theoretically robust representation of jet splittings directly into quantum states on qubits. This mapping supports a Quantum Tree-Topology Network that follows the natural hierarchical structure of the Lund tree rather than treating data as a flat vector. On benchmarks for W boson, top quark, and polarization tagging, the resulting network reaches accuracy comparable to much larger classical deep networks such as LundNet. It also shows stronger performance than standard quantum encodings in low-data settings and reduced sensitivity to differences between parton-shower models.

Core claim

The LP2B encoding maps the Lund plane representation of jet kinematics directly into qubit states. Leveraging this encoding, the Quantum Tree-Topology Network natively embeds the hierarchical structure of the Lund tree and matches the performance of large classical deep learning architectures such as LundNet on polarization tagging while remaining competitive for W boson and top quark tagging. The network requires three orders of magnitude fewer parameters than LundNet, demonstrates enhanced sensitivity relative to standard 1P1Q encodings, outperforms classical methods in the low-data regime, and is less susceptible to overfitting generator-specific parton shower and hadronization models. It

What carries the argument

The Lund Plane to Bloch (LP2B) encoding, which converts the theoretically clean Lund plane jet representation into qubit states, together with the Quantum Tree-Topology Network (QTTN) that embeds the Lund tree hierarchy.

If this is right

  • The small parameter count opens the possibility of low-latency FPGA implementations suitable for real-time trigger systems at colliders.
  • Superior low-data performance makes the approach viable for analyses with limited statistics.
  • Reduced dependence on specific generator models implies smaller systematic uncertainties when applied to real collision data.
  • The architecture pushes the performance-per-parameter frontier relative to MLPs and BDTs of similar size.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the encoding generalizes, similar tree-topology networks could be applied to other hierarchical data structures common in high-energy physics analyses.
  • The reduced overfitting to shower models suggests quantum models may require less extensive calibration campaigns than classical deep networks when moving from simulation to data.
  • Validation on a 3-qubit device indicates the method is already testable on present-day hardware, though larger qubit counts will be needed to scale to full jet substructure problems.

Load-bearing premise

The LP2B mapping preserves all tagging-relevant information from the Lund plane without meaningful loss when states are prepared on near-term quantum hardware.

What would settle it

An experiment in which the QTTN accuracy on a large, held-out dataset falls well below that of a classical network of comparable parameter count after identical training on the same Lund-plane inputs.

Figures

Figures reproduced from arXiv: 2604.18613 by Fabrizio Napolitano, Livio Fan\`o, Luca Della Penna, Tommaso Tedeschi.

Figure 1
Figure 1. Figure 1: A visualization of the Lund Jet Plane repres [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: 3.1.2 Variational Entanglement and Node Updates Following the state preparation, the network undergoes L layers of parameterized quantum operations designed to entangle the nodes and extract hierarchical correla￾tions. The entanglement topology is constrained by the physical edges of the C/A declustering tree. To allow information to flow from the leaves (the latest splittings in the cascade) up to the roo… view at source ↗
Figure 2
Figure 2. Figure 2: Difference in the Lund Plane (with two different parametrizations) of the densities ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Geometric visualization of the differentiable [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic representation of the QTTN executed with two layers ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Training dynamics of the QTTN L = 3 for the Gbulk → W+W− process and selected benchmarks over the first 30 epochs, showing the stable minimization of the Binary Cross-Entropy loss alongside the corres￾ponding validation AUC. datasets. However, high-fidelity, full simulations of the detector require vast amounts of computing time, some￾times leading to sizable statistical uncertainty in meas￾urements [31]. … view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of ROC curves for the QTTN and the classical and quantum benchmarks considered in this [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The Pareto front showing complexity (log scale) versus performance, showing the QTTN (in red) defined [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of AUC scores and relative differences for different training data statistics across the considered [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distribution of residuals between hardware [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of ROC curves for the QTTN for the different number of layers considered in this work. [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Gradient saliency for the parameters of the quantum circuit considered in this work, the QTTN (top) [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
read the original abstract

The application of quantum algorithms to jet substructure analysis is of growing interest as NISQ hardware continues to mature in qubit count and gate depth. Jet substructure remains essential for addressing demanding and complementary challenges at the LHC and beyond, notably object classification and polarization tagging. However, existing quantum machine learning approaches typically rely on data representations that suffer from infrared and collinear unsafety, sensitivity to non-perturbative effects, or poor scalability. In this work, we introduce the Lund Plane to Bloch (LP2B) encoding, designed to map a theoretically clean and robust representation of jet kinematics directly into qubit states. Leveraging this encoding, we implement a Quantum Tree-Topology Network (QTTN) that natively embeds the hierarchical structure of the Lund tree. We evaluate the QTTN across multiple benchmarks and observe that it matches the performance of large classical deep learning architectures, such as LundNet, on polarization tagging, while maintaining competitive accuracy for W boson and top quark tagging. The architecture demonstrates enhanced sensitivity compared to standard 1P1Q encodings on both polarization and W tagging, and pushes the Pareto front when compared against MLP of similar size and BDTs. Remarkably, the QTTN requires three orders of magnitude fewer parameters than LundNet, demonstrating promises for low-latency FPGA implementations in trigger systems. Furthermore, the QTTN outperforms classical methods in the low-data regime, making it suitable for low-yield, data-driven analyses. We also find that the quantum model is less susceptible to overfitting generator-specific parton shower and hadronization models than classical deep learning approaches, pointing toward potentially smaller systematic uncertainties. We validate the QTTN on real quantum hardware using a 3-qubit SpinQ device.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces the Lund Plane to Bloch (LP2B) encoding to map the Lund plane representation of jet kinematics directly into qubit states and implements a Quantum Tree-Topology Network (QTTN) that natively embeds the hierarchical structure of the Lund tree. It evaluates the QTTN on polarization tagging, W boson tagging, and top quark tagging benchmarks, claiming performance that matches large classical architectures such as LundNet on polarization tagging while remaining competitive on the other tasks, with three orders of magnitude fewer parameters, improved low-data performance, and reduced susceptibility to generator-specific overfitting. The work also reports validation of the QTTN on a 3-qubit SpinQ quantum device.

Significance. If the performance equivalence, parameter reduction, and hardware results hold after addressing the scaling concerns, the work would provide a concrete demonstration of quantum advantage in parameter efficiency for jet substructure tasks at the LHC, with potential implications for low-latency trigger applications and reduced systematic uncertainties in data-driven analyses.

major comments (2)
  1. [Hardware Validation] Hardware Validation section: The manuscript states that the QTTN is validated on a 3-qubit SpinQ device, yet the LP2B encoding plus tree-topology network for full Lund-plane representations requires a qubit count that scales with the number of splittings or retained features. A 3-qubit circuit can embed only a severely truncated hierarchy; therefore the reported hardware accuracies cannot confirm that the benchmark performance survives noise, limited connectivity, and depth constraints for the complete model.
  2. [Results] Results and benchmarks: The claims that the QTTN 'matches the performance of large classical deep learning architectures, such as LundNet, on polarization tagging' and 'maintains competitive accuracy for W boson and top quark tagging' are presented without accompanying tables, error bars, training details, or explicit comparison metrics visible in the abstract; full verification of data handling and statistical significance is required to support the central performance assertions.
minor comments (1)
  1. [Abstract] Abstract: The term '1P1Q encodings' is used without definition; ensure it is introduced and contrasted with LP2B in the main text for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major point below with clarifications and indicate planned revisions.

read point-by-point responses

  1. Referee: [Hardware Validation] Hardware Validation section: The manuscript states that the QTTN is validated on a 3-qubit SpinQ device, yet the LP2B encoding plus tree-topology network for full Lund-plane representations requires a qubit count that scales with the number of splittings or retained features. A 3-qubit circuit can embed only a severely truncated hierarchy; therefore the reported hardware accuracies cannot confirm that the benchmark performance survives noise, limited connectivity, and depth constraints for the complete model.

    Authors: We agree that the 3-qubit SpinQ validation uses a truncated hierarchy, as the full LP2B+QTTN scales with retained splittings and exceeds current device capacity. The hardware results are presented as a proof-of-principle for the encoding and basic tree topology under real noise, not as validation of the complete benchmark model. We will revise the Hardware Validation section to explicitly state the truncation, clarify the scope, and note that full-model hardware tests await larger devices. revision: partial

  2. Referee: [Results] Results and benchmarks: The claims that the QTTN 'matches the performance of large classical deep learning architectures, such as LundNet, on polarization tagging' and 'maintains competitive accuracy for W boson and top quark tagging' are presented without accompanying tables, error bars, training details, or explicit comparison metrics visible in the abstract; full verification of data handling and statistical significance is required to support the central performance assertions.

    Authors: Detailed tables, figures with error bars, training hyperparameters, data preprocessing, and statistical comparisons (including significance tests) are provided in the Results section and supplementary material. The abstract offers a concise summary. We will revise the abstract to include key quantitative metrics and ensure the main text more explicitly cross-references data handling and statistical procedures for easier verification. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical benchmarks rest on external data and training

full rationale

The manuscript introduces the LP2B encoding and QTTN as new constructions, then reports tagging accuracies, parameter counts, and hardware runs as direct empirical outcomes from training on jet datasets and executing on a SpinQ device. No derivation chain, equation, or self-citation is shown that reduces a claimed result to a fitted input or prior author result by construction. Performance equivalence to LundNet and low-data advantages are presented as observed benchmarks, not as predictions forced by the model definition itself. The 3-qubit validation is a limited test but does not create circularity in the reported metrics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The central claim rests on the domain assumption that the Lund plane is a clean representation and on the empirical success of the new encoding and network; no explicit free parameters or invented entities beyond the proposed methods are detailed in the abstract.

axioms (1)
  • domain assumption Lund plane provides a theoretically clean and robust representation of jet kinematics that is infrared and collinear safe
    Invoked as the basis for the LP2B encoding in the abstract.
invented entities (2)
  • LP2B encoding no independent evidence
    purpose: Map Lund plane jet kinematics directly into qubit states
    Newly introduced mapping in this work
  • QTTN no independent evidence
    purpose: Quantum network that natively embeds the hierarchical Lund tree structure
    New architecture proposed and evaluated in this work

pith-pipeline@v0.9.0 · 5635 in / 1417 out tokens · 45505 ms · 2026-05-10T13:16:36.964474+00:00 · methodology

discussion (0)

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