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  • Open Access

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

Zong-Liang Li1,2 and Shi-Xin Zhang1,*

  • *Contact author: shixinzhang@iphy.ac.cn
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Phys. Rev. Research 8, 013266 – Published 9 March, 2026

DOI: https://doi.org/10.1103/4kyq-n8jb

Abstract

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.

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Phys. Rev. Research 8, 013266– Published 9 March, 2026
  • Received 18 August 2025
  • Revised 4 January 2026
  • Accepted 18 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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