Dual role of low-weight Pauli propagation: A flawed simulator but a powerful initializer for variational quantum algorithms

Variational quantum algorithms are often hindered by rugged optimization landscapes. In this work, we investigate the low-weight Pauli propagation (LWPP) algorithm and find that it serves as an unreliable energy estimator for variational circuits. However, we reveal a counterintuitive insight: The Pauli-weight truncation acts as a spectral filter, effectively smoothing out high-frequency local minima while preserving the global basin of attraction in the landscape. We identify this mechanism as landscape alignment, where the approximate landscape becomes a superior navigator compared to the rugged exact landscape. Benchmarks across diverse spin models and molecular systems demonstrate that LWPP-initialized optimization yields order-of-magnitude improvements in accuracy, often finding solutions inaccessible to direct exact optimization. This work reframes LWPP from a flawed simulator into a vital preoptimizer that serves not only as a cheap classical substitute but also as an essential tool for addressing quantum optimization challenges.