arxiv: 2605.06789 · v1 · submitted 2026-05-07 · 🪐 quant-ph · hep-ph· hep-th

Recognition: 2 theorem links

· Lean Theorem

Physics inspired quantum algorithm for QCD splitting functions

Gabriel Rouxinol , Yacine Haddad , Cenk T\"uys\"uz , Sofia Vallecorsa , Michele Grossi

Authors on Pith no claims yet

Pith reviewed 2026-05-11 00:54 UTC · model grok-4.3

classification 🪐 quant-ph hep-phhep-th

keywords quantum circuitQCD splittingparton showerhelicity entanglementjet substructureevent generationquantum hardware

0 comments

The pith

A two-qubit quantum circuit reproduces the helicity entanglement and momentum sharing of gluon splittings in QCD and composes into multi-prong distributions that match LHC jet data.

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

The authors build a simple quantum circuit to model the quantum correlations that arise when a gluon splits into two gluons. They first calculate the exact amount of entanglement created at the splitting vertex using a standard measure called concurrence. They then design a two-qubit circuit whose rotation angles directly control the momentum fractions carried by the two outgoing gluons while producing the same entanglement pattern predicted by QCD. When several copies of this circuit are placed in sequence, the combined measurement statistics generate the momentum distributions seen in three- and four-prong jets. The circuit is shallow enough to run on present-day superconducting processors, where it yields results consistent with both simulation and experimental data after routine error mitigation.

Core claim

For the pure-gluon channel, we derive an analytic expression for the helicity entanglement generated at the splitting vertex, quantified via the concurrence, and construct a two-qubit circuit whose measurement outcomes encode the momentum shared between outgoing gluons while reproducing the QCD-predicted entanglement structure. Calibrating the circuit parameters to LHC jet substructure data maps reconstructed momentum-sharing fractions to circuit rotation angles. Composing multiple splitting primitives yields multi-prong momentum-fraction distributions; we validate the three- and four-prong cases against experimental data and find good agreement. For the three-prong configuration, we execute

What carries the argument

A modular two-qubit circuit primitive whose parameterized gates encode momentum-sharing fractions and whose output statistics reproduce the concurrence of helicity entanglement at a gluon splitting vertex.

If this is right

Parameters calibrated once on single-splitting data produce multi-prong distributions that agree with measured jet substructure.
The shallow circuit depth allows direct execution on current superconducting hardware with results matching classical simulation after standard quality cuts.
The primitive supplies a physics-informed building block for constructing larger quantum circuits that simulate full parton showers.
Momentum fractions reconstructed from circuit measurements are directly tied to the rotation angles used in the gates.

Where Pith is reading between the lines

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

The same circuit structure could be extended to quark-gluon splitting channels by deriving the corresponding concurrence and adjusting the gate set.
If the composition rule holds at higher multiplicity, the approach offers a route to sampling rare jet configurations on quantum hardware without the exponential cost of classical Monte Carlo.
Jet observables sensitive to helicity correlations might serve as indirect probes of the entanglement generated at each splitting vertex.

Load-bearing premise

The entanglement and momentum mapping derived for one splitting can be directly chained across independent splittings without interference terms or higher-order QCD corrections altering the final distributions.

What would settle it

If the momentum-fraction histograms obtained by composing three or four copies of the calibrated circuit deviate measurably from LHC jet substructure data in the three- or four-prong channels, the composability assumption fails.

read the original abstract

We introduce a modular quantum circuit primitive to model entanglement dynamics in QCD parton splitting and use it as a composable building block for data-driven, physics-consistent event generation. For the pure-gluon channel, we derive an analytic expression for the helicity entanglement generated at the splitting vertex, quantified via the concurrence, and construct a two-qubit circuit whose measurement outcomes encode the momentum shared between outgoing gluons while reproducing the QCD-predicted entanglement structure. Calibrating the circuit parameters to LHC jet substructure data maps, reconstructed momentum-sharing fractions are directly related to circuit rotation angles. Composing multiple splitting primitives yields multi-prong momentum-fraction distributions; we validate the three- and four-prong cases against experimental data and find good agreement. For the three-prong configuration, we execute the circuit on superconducting quantum hardware and obtain results consistent with simulation after standard quality cuts, enabled by the low qubit count and shallow circuit depth. This work provides a concrete framework for quantum-native parton-shower modules that encode quantum correlations at the level of splitting dynamics, and offers physics-informed ans\"atze for future quantum algorithms for QCD.

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.

Desk Editor's Note private letter to a colleague

The paper gives a two-qubit circuit for gluon splitting that matches an analytic concurrence and gets calibrated to jet data, then composes the blocks for multi-prong distributions with a hardware run, but the calibration and independence assumptions need closer checks.

read the letter

The main point is a modular quantum circuit that encodes the helicity entanglement at a gluon splitting vertex through an analytic concurrence, maps momentum fractions to rotation angles, and gets calibrated directly to LHC jet substructure data. Multiple copies are then stacked to produce three- and four-prong momentum distributions that are compared to experiment, with the three-prong case run on superconducting hardware after basic cuts. The circuit is shallow enough that the hardware test is practical. What is actually new is the explicit derivation of concurrence for the pure-gluon channel tied to a simple two-qubit ansatz whose measurement statistics reproduce the QCD momentum sharing, plus the demonstration that these blocks can be composed without extra gates. The hardware execution and the modular framing are concrete steps forward for anyone thinking about quantum-native parton showers. The calibration step works for the single-split case and produces plausible multi-prong shapes after composition. The soft spots are the lack of visible derivation details or error propagation in the summary, and the fact that the same data class used for angle calibration is also used to validate the composed distributions. This raises a real but not fatal risk that agreement reflects the fit rather than independent predictive power. In addition, treating each splitting as uncorrelated ignores color coherence and soft-gluon interference that appear in real QCD, so the composition is an effective model rather than a first-principles reproduction. The paper is aimed at quantum information people who want to apply circuits to high-energy physics and at phenomenologists open to new shower primitives. A reader looking for fresh circuit constructions and small-scale hardware results will find usable material here. It deserves peer review because the core construction is original and the hardware result is verifiable, even if the validation section needs tightening on data separation and interference checks.

Referee Report

3 major / 3 minor

Summary. The manuscript introduces a modular quantum circuit primitive for modeling helicity entanglement in QCD parton splitting. For the pure-gluon channel it derives an analytic concurrence, constructs a two-qubit circuit whose measurement statistics encode the momentum fraction z while matching that concurrence, calibrates the rotation angles to LHC jet substructure data, and composes multiple primitives to generate three- and four-prong momentum-fraction distributions that are reported to agree with experimental data; the three-prong case is also executed on superconducting hardware.

Significance. If the composition of calibrated single-splitting circuits reproduces multi-prong distributions beyond the fitted regime, the framework would supply a concrete, shallow-depth quantum-native module for encoding entanglement at splitting vertices and a physics-informed ansatz for future quantum parton-shower algorithms. The reported hardware execution with low qubit count and standard quality cuts demonstrates practical feasibility on current devices.

major comments (3)

[§2] §2 (analytic concurrence): the claimed closed-form expression for the pure-gluon helicity concurrence is stated without derivation steps, intermediate spinor algebra, or explicit verification that it reduces to the known Altarelli–Parisi kernel in the appropriate limit; this derivation is load-bearing for the assertion that the circuit reproduces the QCD entanglement structure.
[§4] §4 (calibration and multi-prong validation): rotation angles are fitted directly to LHC jet-substructure data to map z; the same primitives are then composed and compared to three- and four-prong distributions drawn from the same experimental class. No out-of-sample test, variation of calibration dataset, or comparison against an unfitted baseline is shown, so the reported agreement cannot yet be distinguished from a post-hoc fit.
[§5] §5 (composition): the multi-prong results rest on the assumption that single-splitting entanglement and momentum sharing remain uncorrelated across successive vertices. No estimate of color-coherence or NLO interference terms is provided, nor is a comparison made to a full QCD shower with the same single-splitting kernel; this assumption is load-bearing for the claim that the composed circuit yields accurate multi-prong distributions.

minor comments (3)

[Abstract] Abstract and §3: the phrase “physics-consistent” is used after data calibration; a brief clarification of what is meant by consistency (e.g., reproduction of the leading-order kernel plus fitted higher-order effects) would avoid ambiguity.
[Hardware section] Hardware results paragraph: the quality cuts applied to the superconducting-device data are mentioned but not quantified; reporting the fraction of shots retained and the effect on the extracted z distribution would strengthen the comparison to simulation.
[Throughout] Notation: the symbols for the calibrated rotation angles and the theoretical circuit angles are not always distinguished; a short table or explicit mapping would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, providing the strongest honest defense and indicating where revisions have been made to the manuscript.

read point-by-point responses

Referee: §2 (analytic concurrence): the claimed closed-form expression for the pure-gluon helicity concurrence is stated without derivation steps, intermediate spinor algebra, or explicit verification that it reduces to the known Altarelli–Parisi kernel in the appropriate limit; this derivation is load-bearing for the assertion that the circuit reproduces the QCD entanglement structure.

Authors: We agree that additional detail on the derivation is warranted. In the revised manuscript we have expanded §2 with the complete step-by-step spinor-algebra derivation of the concurrence and have added an explicit reduction to the Altarelli–Parisi kernel in the classical limit, thereby confirming that the circuit encodes the correct QCD entanglement structure. revision: yes
Referee: §4 (calibration and multi-prong validation): rotation angles are fitted directly to LHC jet-substructure data to map z; the same primitives are then composed and compared to three- and four-prong distributions drawn from the same experimental class. No out-of-sample test, variation of calibration dataset, or comparison against an unfitted baseline is shown, so the reported agreement cannot yet be distinguished from a post-hoc fit.

Authors: The calibration uses single-splitting observables while the multi-prong distributions constitute a test of composability on a different observable. To strengthen the presentation we have added, in the revision, a sensitivity analysis by varying the fitted parameters within their uncertainties and a direct comparison against an unfitted (flat-z) baseline. A fully independent out-of-sample dataset is not available within the current experimental samples, but we now explicitly discuss this limitation. revision: partial
Referee: §5 (composition): the multi-prong results rest on the assumption that single-splitting entanglement and momentum sharing remain uncorrelated across successive vertices. No estimate of color-coherence or NLO interference terms is provided, nor is a comparison made to a full QCD shower with the same single-splitting kernel; this assumption is load-bearing for the claim that the composed circuit yields accurate multi-prong distributions.

Authors: We acknowledge that the modular construction assumes uncorrelated successive splittings. In the revised manuscript we have inserted a paragraph providing an order-of-magnitude estimate of color-coherence and NLO interference effects drawn from the QCD literature, showing they remain small in the kinematic region probed. We have also added a qualitative comparison of the composed-circuit results to a standard parton-shower Monte Carlo that employs the identical single-splitting kernel. revision: yes

Circularity Check

1 steps flagged

Fitted single-splitting circuit parameters composed for multi-prong validation reduces to effective-model fit

specific steps

fitted input called prediction [Abstract]
"Calibrating the circuit parameters to LHC jet substructure data maps, reconstructed momentum-sharing fractions are directly related to circuit rotation angles. Composing multiple splitting primitives yields multi-prong momentum-fraction distributions; we validate the three- and four-prong cases against experimental data and find good agreement."

Rotation angles are fitted to data to encode momentum fractions z at each vertex. The identical calibrated primitives are then composed without additional terms to generate multi-prong distributions that are validated against experimental data, so agreement is forced by the single-splitting fit rather than emerging from the analytic concurrence alone.

full rationale

The analytic derivation of concurrence and the two-qubit circuit construction that reproduces it appear independent of data. However, the load-bearing claim for multi-prong results is the direct composition of primitives whose rotation angles are calibrated to LHC jet substructure data; the reported agreement with three- and four-prong distributions therefore tests the extrapolation of a fitted single-splitting model rather than an unfitted first-principles composition. This matches the 'fitted input called prediction' pattern with partial circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim depends on fitting circuit parameters to experimental data and on the assumption that independent splitting primitives compose without extra quantum corrections.

free parameters (1)

circuit rotation angles
Calibrated to LHC jet substructure data to directly relate to reconstructed momentum-sharing fractions.

axioms (2)

domain assumption QCD splitting functions determine a specific helicity entanglement structure that can be quantified by concurrence
Invoked to derive the analytic expression for the pure-gluon channel.
domain assumption A two-qubit circuit can faithfully reproduce both the momentum distribution and the entanglement of the splitting vertex
Basis for constructing the modular primitive.

invented entities (1)

modular quantum circuit primitive for parton splitting no independent evidence
purpose: Composable building block that encodes quantum correlations for data-driven event generation
New postulated module introduced to enable physics-consistent multi-prong simulations.

pith-pipeline@v0.9.0 · 5510 in / 1562 out tokens · 70964 ms · 2026-05-11T00:54:53.083906+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

For the pure-gluon channel, we derive an analytic expression for the helicity entanglement generated at the splitting vertex, quantified via the concurrence, and construct a two-qubit circuit whose measurement outcomes encode the momentum shared between outgoing gluons while reproducing the QCD-predicted entanglement structure.
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean LogicNat.equivNat unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Composing multiple splitting primitives yields multi-prong momentum-fraction distributions; we validate the three- and four-prong cases against experimental data and find good agreement.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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