Aligning Quantum Operators with Large Language Models

2026-06-11

AI Summary

Current large language models struggle to represent and reason about quantum operators, such as unitary matrices. This work proposes embedding quantum unitary operators into the latent space of a large language model, enabling unified modeling of natural language and quantum operations and endowing the model with native understanding of quantum gate manipulations for the first time. By integrating latent-space embeddings with Clifford+T circuit synthesis and modeling based on Pauli rotation gate sets, the approach supports conditional quantum circuit synthesis from natural language specifications—even for gate constraints unseen during training. Experiments demonstrate state-of-the-art performance on Clifford+T synthesis tasks, with consistent improvements as data scale increases and no evident saturation, offering a novel pathway toward quantum-aware foundation models.

Abstract

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.

Problem

• quantum operators
• large language models
• unitary matrices
• quantum representations
• symbolic reasoning

Innovation

• quantum operators
• large language models
• latent space alignment
• language-conditioned synthesis
• Clifford+T synthesis