Separating quantum circuits from classical LLMs

2026-08-04

AI Summary

This work investigates the computational boundaries of constant-depth quantum circuits (QNC⁰) compared to restricted classical large language models in prediction and generation tasks. By constructing specific distributions and functions and leveraging complexity-theoretic arguments alongside structural analysis of language models, the study establishes the first unconditional quantum advantage separation in the context of large language models. It demonstrates that there exist distributions efficiently samplable by QNC⁰ circuits that cannot be approximately sampled by shallow diffusion-based language models. Furthermore, it identifies an explicit function requiring super-polynomial decoder width for Transformer-based models to compute, while being efficiently realizable by QNC⁰ or slightly stronger QNC⁰[log log n] circuits.

Abstract

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.

Problem

• quantum advantage
• large language models
• QNC circuits
• distributional separation
• functional separation

Innovation

• quantum advantage
• QNC circuits
• diffusion language models
• transformer separation
• computational complexity