The Dual Role of Low-Weight Pauli Propagation: A Flawed Simulator but a Powerful Initializer for Variational Quantum Algorithms

Variational quantum algorithms (VQAs) rely on a classical optimizer to tune a parameterized quantum circuit, raising the question of whether classical methods can assist in this process. In this work, we investigate the low-weight Pauli propagation (LWPP) algorithm as a potential classical tool for simulating the VQA circuit. We first find that LWPP is an unreliable estimator of the true energy, limiting its utility as a direct simulator. However, we uncover its real value: despite this numerical inaccuracy, its approximate optimization landscape robustly guides parameters toward high-quality basins of attraction. We therefore propose harnessing LWPP not for simulation, but as a classical pre-optimizer to find superior initial parameters for the main VQA loop. Benchmarking this strategy on Heisenberg models, we demonstrate a remarkable enhancement in both the final accuracy and convergence rate, typically by an order of magnitude, over standard heuristics. Our work thus reframes LWPP from a flawed simulator into a powerful classical pre-processor that effectively mitigates the notorious optimization challenges in VQAs and reduces the computational burden on near-term quantum hardware.