Physics inspired quantum algorithm for QCD splitting functions

The gist: This work introduces 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.

Role of Entanglement in QCD Splitting

The study focuses on the pure-gluon channel for the g → gg interaction because of its uniqueness in QCD relative to Quantum Electrodynamics due to the non-abelian nature of the SU(3) gauge group and its dominant role in high transverse momentum parton shower evolution at the LHC, especially via the gg → ggg interaction The study focuses on the pure-gluon channel for the g → gg interaction because of its uniqueness in QCD relative to Quantum Electrodynamics due to the non-abelian nature of the SU(3) gauge group and its dominant role in high transverse momentum parton shower evolution at the LHC, especially via the gg → ggg interaction.

The computation of scattering amplitudes for all possible three-point gluon interactions is governed by the interaction term present in the SM Lagrangian The computation of scattering amplitudes for all possible three-point gluon interactions is governed by the interaction term present in the SM Lagrangian. The average scattering amplitude is found to be M2 ≡ 1/2 1/8 X color X helicity M2 = 8CA4g 2/16 E 2θ squared 1 + z 4 + (1 − z) 4 = = 6g 2E 2θ squared / The average scattering amplitude is found to be M2 ≡ 1/2 1/8 X color X helicity M2 = 8CA4g 2/16 E 2θ squared 1 + z 4 + (1 − z) 4 = = 6g 2E 2θ squared /.

Quantum Circuit for QCD Splitting

A two-qubit quantum circuit is designed to encode the momentum fractions z and 1−z for a g → gg splitting, enforcing the entanglement computed in the previous section while having measurement outcome probabilities match those given by the splitting function To achieve this, we design the quantum circuit of Fig. 2, encoding it in a way that the splitting fraction of the interaction, z, is the expected value of the third Pauli matrix σ3 of the first qubit, meaning a = z, and consequently, the expected value of σ3 of the second qubit is b = 1 − z The circuit is designed to encode momentum fractions z and 1−z for a g → gg splitting, enforcing the entanglement computed in the previous section while having measurement outcome probabilities match those given by the splitting function.

The circuit US(z(γ1, γ3)) acts as a splitting primitive: given a parent parton encoded in one qubit and an ancilla initialized to 0⟩, it outputs two qubits whose σ3-expectation values encode the daughter momentum fractions and whose entanglement is consistent with the QCD prediction for splitting fraction z The circuit US(z(γ1, γ3)) acts as a splitting primitive: given a parent parton encoded in one qubit and an ancilla initialized to 0⟩, it outputs two qubits whose σ3-expectation values encode the daughter momentum fractions and whose entanglement is consistent with the QCD prediction for splitting fraction z.

Data-Driven Calibration

The circuit parameters are determined by calibrating it to LHC jet substructure data, specifically using the AspenOpenJets dataset [44] to extract momentum-sharing fractions from reconstructed jets From this dataset, we obtain a dataset of momentum fractions for each event and determine the pairs of values (γ1,i, γ3,i), such that zi = z(γ1,i, γ3,i) and Ccircuit(γ1,i, γ3,i) = CQCD(zi) This constitutes a two-equation system with two variables which can be solved numerically After obtaining the parameter distribution, we implement it with Pennylane [84] and study its properties.

Composability and Validation

The circuit is designed so that successive applications are identical to successive splittings, producing the momentum fractions of the final partons Multi-prong structures arise by iterating this primitive on the parton’s qubit with the highest momentum fraction, implemented by CNOT gates that propagate the parent’s momentum fraction into the next splitting stage We first consider the application of two successive splittings with fractions z and z′, as presented in Fig. 4, to get the momentum fraction of three final prongs The results were obtained from 500 independent circuit executions with 1024 shots of the quantum circuit, using independently sampled parameters from Sec. 3.2 The three-prong momentum fraction distributions were obtained both with the quantum circuit running on an ideal quantum simulator and on ibm Marrakesh hardware.

Conclusion and Future Directions

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 ansätze for future quantum algorithms for QCD Despite its proof-of-concept nature, essential elements of a complete formulation remain to be developed The parton shower process depends on using the Sudakov factor to update the virtuality of the incoming particle Moreover, one must consider the different parton species involved in a shower, an aspect that the real data we used do not account for Overall, this work provides a first step toward building simulations in which the role of quantum entanglement is physically motivated in the design.

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The gist: This paper introduces 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.

Role of Entanglement in QCD Splitting

The study focuses on the pure-gluon channel for the g → gg interaction because of its uniqueness in QCD relative to Quantum Electrodynamics due to the non-abelian nature of the SU(3) gauge group and its dominant role in high transverse momentum parton shower evolution at the LHC, especially via the gg → ggg interaction The computation of scattering amplitudes for all possible three-point gluon interactions is governed by the interaction term present in the SM Lagrangian. The average scattering amplitude is found to be M2 ≡ 1/2 1/8 X color X helicity M2 = 8CA4g 2/16 E 2θ squared 1 + z 4 + (1 − z) 4 = = 6g 2E 2θ squared /.

Quantum Circuit for QCD Splitting

A two-qubit quantum circuit is designed to encode the momentum fractions z and 1−z for a g → gg splitting, enforcing the entanglement computed in the previous section while having measurement outcome probabilities match those given by the splitting function The circuit US(z(γ1, γ3)) acts as a splitting primitive: given a parent parton encoded in one qubit and an ancilla initialized to 0⟩, it outputs two qubits whose σ3-expectation values encode the daughter momentum fractions and whose entanglement is consistent with the QCD prediction for splitting fraction z.

Data-Driven Calibration

The circuit parameters are determined by calibrating it to LHC jet substructure data, specifically using the AspenOpenJets dataset [44] to extract momentum-sharing fractions from reconstructed jets From this dataset, we obtain a dataset of momentum fractions for each event and determine the pairs of values (γ1,i, γ3,i), such that zi = z(γ1,i, γ3,i) and Ccircuit(γ1,i, γ3,i) = CQCD(zi) This constitutes a two-equation system with two variables which can be solved numerically.

1. The improved AI system can generate physics-consistent event data by utilizing a quantum-native, modular splitting unit for the g → gg channel that enforces kinematic consistency via total momentum conservation and momentum fraction ordering. This allows the AI to produce multi-prong momentum-fraction distributions validated against experimental LHC data, as shown in Section 3.2 and Figure 15.

2. The system can directly map reconstructed jet kinematics to quantum circuit parameters by solving a two-equation system with two variables where zi = z(γ1,i, γ3,i) and Ccircuit(γ1,i, γ3,i) = CQCD(zi). This enables the AI to calibrate its splitting primitives based on data like the AspenOpenJets dataset to ensure the circuit reproduces the empirical z-distribution of the two-prong jets and its concurrence agrees with the prediction from QCD.

3. The AI can execute complex parton shower evolutions by implementing successive applications of this primitive, where the measured expectation values propagate multiplicatively to yield momentum fractions for three-prong and four-prong topologies. This provides a composable route to shower-like multi-prong structures.

4. The system can perform physics-informed model training by treating the circuit parameters as trainable variables in a variational framework, allowing it to encode non-perturbative corrections into the entanglement structure of the physics-motivated splitting circuit through QML approaches.

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 modelling of parton-shower kinematics. 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 σ 3 expectation values encode the momentum shared between outgoing gluons. The circuit reproduces the QCD-predicted concurrence by construction, which fixes a two-qubit correlator that the momentum fractions alone do not determine. Iterating the primitive, the concurrence obeys a product rule across successive splittings. Calibrating the circuit parameters to LHC jet substructure data relates the reconstructed momentum-sharing fractions directly to circuit rotation angles. Composing multiple splitting primitives yields multi-prong momentum-fraction distributions; we compare the three- and four-prong cases against experimental data, reproducing the core of the distributions. For the three-prong configuration, we execute the circuit on superconducting quantum hardware, recover the momentum-fraction distributions after a device-bias correction calibrated on a held-out subset, and study how noise alters the entanglement-dependent observable. 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 ansätze for future quantum algorithms for QCD.