Physics Inspired Quantum Algorithm for QCD Splitting Functions

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 ansätze for future quantum algorithms for QCD.