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

TL;DR

This paper reveals that low-weight Pauli propagation, despite being an unreliable energy estimator, acts as a spectral filter that improves variational quantum algorithm optimization by smoothing the landscape, leading to better solutions.

Contribution

It uncovers the dual role of LWPP as a landscape smoother and initializer, transforming it from a flawed simulator into a powerful pre-optimizer for quantum algorithms.

Findings

LWPP acts as a spectral filter smoothing the optimization landscape.

LWPP-initialized optimization achieves order-of-magnitude accuracy improvements.

Benchmark results show LWPP enables solutions inaccessible to direct optimization.

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.