Quantum-enhanced Large Language Models on Quantum Hardware via Cayley Unitary Adapters
Authors: Borja Aizpurua, Sukhbinder Singh, Augustine Kshetrimayum, Saeed S. Jahromi, Roman Orus
Organizations: Multiverse Computing, Parque Científico y Tecnológico de Gipuzkoa, Paseo May 7 de Miramón 170, 20014, Donostia / San Sebastián, Spain · Department of Basic Sciences, Tecnun – University of Navarra, San Sebastián, Spain · Multiverse Computing, Centre for Social Innovation, 192 Spadina Avenue, ON M5T 2C2, Toronto, Canada · Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20018, San Sebastián, Spain · Ikerbasque Foundation for Science, Maria Diaz de Haro 3, 48013, Bilbao, Spain
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.
Can Large Language Models (LLMs) understand and reason about quantum operators? Despite their remarkable capabilities in mathematics and symbolic reasoning, LLMs remain inherently blind to quantum representations such as unitary matrices. In this work, we take a step toward bridging this gap by introducing an approach that maps unitary operators into the latent space of an LLM, enabling unified modeling over quantum and linguistic inputs. We instantiate this idea on Clifford+T circuit synthesis over a Pauli rotation gate set, where our model achieves results competitive with state-of-the-art methods and scales consistently with training data, with no signs of saturation. Our approach further enables language-conditioned synthesis, allowing gate constraints unseen during training to be specified directly in natural language. This work suggests a path toward quantum--aware foundation models that can natively interpret and reason about quantum operations, which could have broader implications reaching across quantum compilation and algorithm discovery.
Quantum computing provides a powerful paradigm for representing and transforming high-dimensional information through superposition, entanglement, and measurement-induced nonlinear features. While current quantum hardware is not yet practical for direct large-scale vision-language model (VLM) inference, simulated quantum computation can be used during model construction to generate structured parameters for compact classical AI systems. We build RiverONE, a lightweight vision-language model for quantum calibration plot understanding, using simulated quantum computation. It employs a specialized visual encoder and an InternVL-based language backbone. To compensate for compression-induced information loss, we introduce quantum-generated parameters, which are materialized as classical tensors after training. This allows RiverONE to run entirely on classical GPUs at inference time, with no quantum hardware or runtime quantum simulation. With approximately 1.9 billion parameters, RiverONE achieves at least 95% of the performance of NVIDIA Ising Calibration 1 on quantum calibration plot understanding tasks while using less than 10% of its parameter count. These results suggest that simulated quantum computation can serve as a practical construction-stage mechanism for building lightweight, knowledge-intensive scientific VLMs. Our code is available at https://github.com/THeWakeSystems/RiverOne.
Large language models (LLMs) exhibit abilities beyond natural language modelling and text generation. Recent advances in their reasoning capabilities have spurred interest in applying LLMs to complex scientific tasks requiring deep domain expertise and sophisticated reasoning. Quantum computing, as a highly specialised field with significant knowledge barriers and hardware constraints, could greatly benefit from such advancements. However, a key open question that first must be answered is: How can we develop fine-tuning pipelines that instil genuine quantum reasoning in LLMs, rather than task-specific pattern matching? We study this question through quantum circuit simulation as a training objective, where the model must predict the measurement probability distribution resulting from a sequence of quantum gate operations. We propose and compare two fine-tuning pipelines: (1) Supervised Fine-Tuning (SFT) on explicit gate-by-gate state-vector simulation traces, and (2) a two-stage SFT+Group Relative Policy Optimisation (GRPO) approach that sequentially applies SFT followed by GRPO with verifiable rewards. Our findings show that SFT achieves near-perfect in-distribution and gate-count extrapolation accuracy, significantly outperforming both the base model and the GPT-OSS-120B baseline. SFT+GRPO trades some in-distribution precision for better generalisation to larger qubit systems that SFT alone cannot handle. Both pipelines significantly outperform the baselines, demonstrating that targeted fine-tuning on explicit reasoning traces is an effective strategy for advancing quantum reasoning in LLMs.