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

Abstract

Variational quantum algorithms are often hindered by rugged optimization landscapes. In this Letter, 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 pre-optimizer that serves not only as a cheap classical substitute but also as an essential tool for addressing quantum optimization challenges.

4.5 pages, 5 figures with Supplemental Materials

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