Precision-Elastic Persistent Stochastic Execution for Quantum Circuit Simulation

Quantum circuit simulation is usually evaluated through final numerical accuracy, while the dynamics of stochastic execution itself are less explicitly characterized. This work presents a precision-elastic persistent stochastic execution framework based on integral stochastic computing (ISC), where execution behavior is controlled by stream length N and ISC multiplicity m, where m represents the number of aggregated stochastic sub-streams per cycle (standard SC corresponds to m = 1). We focus on correlation-sensitive propagation under persistent reuse, and show that this regime produces circuit-dependent stochastic behavior and execution uncertainty patterns that are not captured by stage-wise re-encoded execution alone. To characterize this behavior, we use high-m tail descriptors, including the circuit-dependent coefficient ${\gamma }_c$, as compact indicators of persistent stochastic sensitivity. Across benchmark circuits, persistent execution exhibits reproducible tail regimes and structured cross-circuit variability, while deterministic reduced-precision baselines are used only as trend-consistency references. We further demonstrate adaptive stochastic precision scheduling, where circuit-dependent $(N,m)$ settings satisfy a target fidelity with reduced stochastic workload. These results position persistent ISC as a configurable stochastic execution framework for analyzing execution-induced uncertainty propagation and correlation-sensitive behavior in quantum circuits.