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 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.