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 textsfQNC0 circuits (i.e., a family of constant-depth quantum circuits consisting of bounded fan-in gates) that no constant-round diffusion language model (textsfDLM) 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 textsfDLMs rely on. 2. Functional separation. We exhibit a function computable in land circ textsfQNC0[loglog n] (i.e., a family of O(loglog n)-depth textsfQNC0 circuits, where n is the input length, followed by a single classical mathsfAND gate) such that any constant-depth decoder-only transformer computing the function must be large: it would have to have width nOmega(1). Together, our work initiates the study of quantum advantage in the era of large language models.