# Quantum-enhanced Large Language Models on Quantum Hardware via Cayley Unitary Adapters

arXiv: https://arxiv.org/abs/2605.05914 · HTML: https://mlsanity.com/paper/2605.05914/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 25 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 15 of 15)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Group](https://mlsanity.com/paper/1901.08428/) (2019)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [Foundations for Near-Term Quantum Natural Language Processing](https://mlsanity.com/paper/2012.03755/) (2020)
- [Quantum Large Language Models via Tensor Network Disentanglers](https://mlsanity.com/paper/2410.17397/) (2024)
- [Quantum-Enhanced Natural Language Generation: A Multi-Model Framework with Hybrid Quantum-Classical Architectures](https://mlsanity.com/paper/2508.21332/) (2025)

## Built on by (most cited first, 1 of 1)

- [Circuit Hypernetworks for Quantum-Augmented Diffusion Language Models](https://mlsanity.com/paper/2609.24657/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have transformed artificial intelligence, yet classical architectures impose a fundamental constraint: every trainable parameter demands classical memory that scales unfavourably with model size. Quantum computing offers a qualitatively different pathway, but practical demonstrations on real hardware have remained elusive for models of practical relevance. Here we show that Cayley-parameterised unitary adapters -- quantum circuit blocks inserted into the frozen projection layers of pre-trained LLMs and executed on a 156-qubit IBM Quantum System Two superconducting processor -- improve the perplexity of Llama 3.1 8B, an 8-billion-parameter model in widespread use, by 1.4% with only 6,000 additional parameters and end-to-end inference validated on real Quantum Processing Unit (QPU). A systematic study on SmolLM2 (135M parameters), chosen for its tractability, reveals monotonically improving perplexity with unitary block dimension, 83% recovery of compression-induced degradation, and correct answers to questions that both classical baselines fail -- with a sharp noise-expressivity phase transition identifying the concrete path to quantum utility at larger qubit scales.