量子QNC^0能采的分布，扩散LM加CoT也采不出；Transformer要宽度n^Ω(1)才够。
该论文证明低深度量子电路与经典语言模型之间存在无条件分离。作者构造了一个可由QNC^0电路采样的分布，任何常数轮扩散语言模型（DLM）即使允许链式思考（CoT）和输出token重掩码，也无法在常数距离内采样它。论文还给出一个由∧∘QNC^0[log log n]计算的函数，任何常数深度decoder-only transformer计算它时宽度需达到n^{Ω(1)}。
Separating quantum circuits from classical LLMs
Modern large language models - transformers and diffusion language models - are built around two canonical algorithmic tasks: prediction and generation. We prove unconditional separations between low-depth quantum computation and the corresponding bounded-resource classical language-model architectures in both regimes. Concretely, we exhibit the following: 1. Distributional separation. We give a distribution that is sampleable by $\textsf{QNC}^0$ circuits (i.e., a family of constant-depth quantum circuits consisting of bounded fan-in gates) that no constant-round diffusion language model ($\textsf{DLM}$) with shallow scheduling and denoising can sample within constant distance, even when allowed sublinear chain-of-thought and output-token revision/remasking events, the very features modern $\textsf{DLM}$s rely on. 2. Functional separation. We exhibit a function computable in $\land \circ \textsf{QNC}^0[\log\log n]$ (i.e., a family of O$(\log\log n)$-depth $\textsf{QNC}^0$ circuits, where $n$ is the input length, followed by a single classical $\mathsf{AND}$ gate) such that any constant-depth decoder-only transformer computing the function must be large: it would have to have width $n^{Ω(1)}$. Together, our work initiates the study of quantum advantage in the era of large language models.