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:
- Distributional separation. We give a distribution that is sampleable by 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 (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 DLMs rely on.
- Functional separation. We exhibit a function computable in \land \circ QNC^0[\log\log n] (i.e., a family of O(\log\log n)-depth QNC^0 circuits, where n is the input length, followed by a single classical 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.