Estimating Local Observables via Cluster-Level Light-Cone Decomposition

Simulating large quantum circuits on hardware with limited qubit counts is often attempted through methods like circuit knitting, which typically incur sample costs that grow exponentially with the number of connections cut. In this work, we introduce a framework based on Cluster-level Light-cone analysis that leverages the natural locality of quantum workloads. We propose two complementary algorithms: the Causal Decoupling Algorithm, which exploits geometric disconnections in the light cone for sampling efficiency, and the Algebraic Decomposition Algorithm, which utilizes algebraic expansion to minimize hardware requirements. These methods allow simulation costs to depend on circuit depth and connectivity rather than system size. Together, our results generalize Lieb-Robinson-inspired locality to modular architectures and establish a quantitative framework for probing local physics on near-term quantum devices by decoupling the simulation cost from the global system size.