Quantum circuits provably beat transformers and diffusion models

Constant-depth quantum circuits can do two things no constant-depth transformer or diffusion language model can match, an arXiv paper proves unconditionally.

That caps a scaling story a lot of people treat as infinite. One proof shows a function built from an O(log log n)-depth quantum circuit plus one AND gate. Any constant-depth transformer computing it needs width that grows as n^Ω(1). More width, not more layers, is the only way a fixed-depth model keeps up.

The other proof targets diffusion language models directly. It shows a distribution that constant-depth quantum circuits can sample. No constant-round diffusion model can match it within constant distance, not even with shallow denoising schedules, sublinear chain-of-thought, or token revision and remasking.

Both results are unconditional. Rare, for this field. Most separations in complexity theory lean on unproven assumptions, like P not equaling NP. These don't, which is what makes the paper stand out even before you get to what it's separating.

The paper doesn't say what happens once transformer or diffusion depth is allowed to grow with input size instead of staying fixed. That's a different regime with different rules, and it's the regime real production models arguably live in.

My take: depth, not scale, is the wall these proofs describe. Feeding a fixed-depth model more chain-of-thought tokens or more remasking passes doesn't get around either result, both hold with those add-ons already in play. Worth watching whether follow-up work pushes these separations into the depth-grows-with-input regime, where most deployed models actually sit. It posted to arXiv in August 2026.