A Practical Guide to using Pauli Path Simulators for Utility-Scale Quantum Experiments

We introduce a low-cost protocol for estimating runtime and memory requirements of Pauli Path Simulators (PPS) in large-scale quantum experiments. Beyond using PPS for reproducing known results, we propose a framework to assess when PPS can enable scientific discovery on its own. We start by analyzing the dynamics of the distributions of Pauli coefficients tracked in the Heisenberg picture and find surprisingly generic convergence features of these distributions as a function of simulation time. We also find certain regularities that allow for extrapolation of memory and runtime requirements for decreasing values of the coefficient truncation parameter δ. We then introduce a framework for studying the convergence of observable expectation values as a function of δ. By combining this framework with our runtime analysis, we propose bifurcating quantum simulation problems broadly into two classes: based on whether or not there is apparent convergence of expectation values as a function of δ. In the absence of rigorous error bounds, this serves as a way for practitioners to understand where their problem falls on the frontier of classical simulability. In cases without apparent convergence, PPS may still serve as a Monte Carlo-like estimate. Applied to IBM's utility-scale experiments, we show parameter regimes where both behaviors are realized. Some of our key findings challenge conventional intuition: reducing δ does not always improve accuracy, and deeper quantum circuits may actually be easier to simulate than shallower ones. Our analysis provides the first systematic approach to assess PPS reliability without assuming a ground truth quantum answer. The BlueQubit SDK implementing these methods has been released publicly, offering researchers a comprehensive toolkit for evaluating this frontier classical simulation approach. These results establish practical guidelines for when PPS can serve as a reliable verification tool versus when it should be used as a complementary estimate alongside quantum experiments.