Analyzing the impact of noise is of fundamental importance to understand the advantages provided by quantum systems. While the classical simulability of noisy discrete-variable systems is increasingly well understood, noisy bosonic circuits are more challenging to simulate and analyze. Here, we address this gap by introducing the $\textit{displacement propagation}$ algorithm, a continuous-variable analogue of Pauli propagation for simulating noisy bosonic circuits. By exploring the interplay of noise and quantum resources, we identify several computational phase transitions, revealing regimes where even modest noise levels render bosonic circuits efficiently classically simulable. In particular, our analysis reveals a surprising phenomenon: computational resources usually associated with bosonic quantum advantage, namely non-Gaussianity and symplectic coherence, can make the system easier to classically simulate in presence of noise.

翻译：分析噪声的影响对于理解量子系统所提供的优势至关重要。尽管含噪声离散变量系统的经典可模拟性已日益明晰，但含噪声玻色电路的模拟与分析更具挑战性。本文通过引入$\textit{位移传播}$算法来填补这一空白，该算法是用于模拟含噪声玻色电路的连续变量类比于泡利传播的方法。通过探究噪声与量子资源的相互作用，我们识别出若干计算相变，揭示了即使中等噪声水平也能使玻色电路高效经典可模拟的区域。特别地，我们的分析揭示了一个令人惊讶的现象：通常与玻色量子优势相关的计算资源——即非高斯性与辛相干性——在噪声存在时反而可能使系统更易于经典模拟。