Implementing Pearl's DO-Calculus on Quantum Circuits: A Simpson-Type Case Study on NISQ Hardware

Distinguishing correlation from causation is a central challenge in machine intelligence, and Pearl's DO-calculus provides a rigorous symbolic framework for reasoning about interventions. A complementary question is whether such intervention logic can be given executable semantics on physical quantum devices. Our approach maps causal networks onto quantum circuits, where nodes are encoded in qubit registers, probabilistic links are implemented by controlled-rotation gates, and interventions are realized by a structural remodeling of the circuit -- a physical analogue of Pearl's ``graph surgery'' that we term circuit surgery. We show that, for a family of 3-node confounded treatment models (including a Simpson-type reversal), the post-surgery circuits reproduce exactly the interventional distributions prescribed by the corresponding classical DO-calculus. We then demonstrate a proof-of-principle experimental realization on an IonQ Aria trapped-ion processor and a 10-qubit synthetic healthcare model, observing close agreement between hardware estimates and classical baselines under realistic noise. We do not claim quantum speedup; instead, our contribution is to establish a concrete pathway by which causal graphs and Pearl-style interventions can be represented, executed, and empirically tested within the formalism of quantum circuits.