Abstract We present Quantum2Prompt , a cross-modal framework that reformulates quantum circuits as structured language prompts, enabling large language models (LLMs) to estimate outcomes of the Variational Quantum Linear Solver (VQLS). Instead of relying on iterative quantum--classical loops with repeated measurements, Quantum2Prompt translates gate sequences, control--target relations, and rotation parameters into compact textual descriptions that preserve circuit semantics while remaining hardware-agnostic. An LLM-based regressor consumes these descriptions to produce real-valued residual estimates, transforming VQLS outcome prediction into a prompt-to-residual regression task. Extensive experiments across Toeplitz, Laplacian, and sparse matrix families show that Quantum2Prompt achieves up to ((R^2 = 0.99)) and MSE = 0.0026 , substantially outperforming classical baselines such as Random Forest, SVR, and LightGBM. Ablation and noise-robustness analyses further demonstrate that combining circuit text, rotation parameters, and optimization-step features yields the most accurate and noise-resilient predictions. Beyond empirical gains, we contribute the first benchmark dataset aligning VQLS circuits, textual encodings, and residual labels, enabling reproducible evaluation and hybrid quantum--language workflows. These results suggest that LLMs can serve as efficient, interpretable surrogates for variational solvers, paving the way toward language-driven quantum algorithm design and performance prediction.The full dataset and implementation are publicly available for reproducibility.
Quantum control is essential for quantum information science and technology, yet designing high-fidelity control protocols remains challenging due to complex optimization landscapes, hardware noise, and long pulse sequences. Existing numerical solvers often require problem-specific engineering and produce opaque control amplitudes, while naive large language models (LLMs) lack the physical consistency and long-horizon precision for reliable quantum control synthesis. Here we introduce VF-QCTRL, a physics-informed large language model framework for general quantum control that combines symbolic reasoning with optimization to propose analytic control ansätze and coherently refine their parameters through feedback. To systematically evaluate LLM-driven quantum control, we develop QCTRL-BENCH, a benchmark spanning sixteen tasks across single- and multi-qubit systems, closed and open quantum dynamics, noiseless and noisy settings, and both analytic and numerical protocols. Across the benchmark, VF-QCTRL demonstrates strong universality, accuracy, efficiency, and interpretability: it applies to generic quantum control systems without task-specific training, achieves performance competitive with or exceeding state-of-the-art conventional solvers in both noiseless and noisy regimes with query efficiency, exhibits favorable inference-time scaling and pulse resolution scaling, and derives physically interpretable analytical protocols directly from prompts. Our results establish physics-informed LLM-based quantum control as a promising paradigm for accurate, efficient, interpretable, and training-free quantum control protocol design across a broad range of quantum systems.
The design of high performing quantum circuits remains largely dependent on human expertise. We introduce an autonomous agentic framework that employs large language models (LLMs) to conduct iterative quantum circuit designs under explicit design constraints. Our system integrates seven components: Exploration, Generation, Discussion, Validation, Storage, Evaluation, and Review. These components form a closed-loop workflow that combines web-based knowledge acquisition, literature-grounded critique, executable code generation, and experimental feedback. We evaluate the framework on two tasks: quantum feature map construction for quantum machine learning and ansatz generation for variational quantum eigensolver applications in quantum chemistry. In image classification benchmarks, the best generated feature map outperforms representative quantum feature maps and, when scaled to larger qubit counts, surpasses the classical radial basis function kernel. In molecular ground state estimation across seven molecules, the generated ansatz attains competitive accuracy with widely used chemically inspired and hardware-efficient constructions while satisfying the imposed scaling constraints. These results establish LLM driven agentic system as a viable paradigm for automated quantum circuit design and illustrate how AI systems can participate in iterative scientific optimization workflows across scientific domains.
The Variational Quantum Linear Solver (VQLS), a hybrid quantum-classical algorithm for solving linear systems, faces a practical scalability bottleneck: the Linear Combination of Unitaries (LCU) decomposition requires
O(L2) circuit evaluations per optimizer iteration, where
L can grow to
4n in the worst case for an
n-qubit system. We address this computational bottleneck through two complementary strategies. First, we present a distributed VQLS (D-VQLS) framework (https://code.ornl.gov/olcf-qcfd/DVQLS.git), built on NVIDIA CUDA-Q, that enables asynchronous, scalable distribution of the
O(L2) cost evaluations. Second, a fast Walsh--Hadamard transform (FWHT)-based Pauli decomposition with coefficient-amplitude pruning threshold
τ=0.01 curbs LCU growth for the structured Toeplitz family, reducing
L from
O(2n) to 64 for
n>6 and compressing the circuit complexity per optimizer iteration from
O(n4n) to
O(n). We derive the exact top-
L Frobenius error and connect it to worst-case solution error. For a 10-qubit tridiagonal Toeplitz system, the
L=64 pruning yields a
256× reduction---from 23 million to 90k circuits per optimizer iteration.
The D-VQLS framework is validated on the NERSC Perlmutter supercomputer using multi-node, multi-GPU ideal state-vector simulations, achieving over
99.99% fidelity against classical solutions on tridiagonal Toeplitz and Hele--Shaw flow benchmarks, with near-ideal strong scaling up to 24 GPUs and
95.3% weak scaling efficiency at 96 GPUs processing more than 360k circuits per optimizer iteration (from larger-
L pruning) for the 10-qubit system. Systematic profiling identifies the optimal resource allocation for distributed quantum circuit workloads, yielding a
2.52× speedup for the configurations studied.
Abstract Variational quantum linear solvers (VQLSs) are a promising class of hybrid quantum--classical algorithms for solving linear systems on near-term quantum devices. However, the performance of VQLSs is often impeded by barren plateaus, particularly when using randomly initialized variational quantum circuits (VQCs). To mitigate this issue, we propose \textit{PVLS}, a GNN-based parameter initialization framework that improves both convergence speed and final solution quality. By reformulating the linear system
Ax=b as a graph with
A encoded in the edges and
b as node features, PVLS learns to predict effective initial VQC parameters. Our method is trained on thousands of randomly generated matrices with varying dimensions (
n∈[4,10]), using optimized VQC parameters as ground-truth labels. On unseen test instances, PVLS reduces the initial cost by an average of 81.3\% and the final loss by 71\% compared to random initialization. PVLS also accelerates convergence, reducing the number of optimization steps by more than 60\% on average. We further evaluate PVLS on ten real-world sparse matrices, demonstrating its generalization capability and robustness. Our results highlight the utility of machine-learned priors in improving the trainability of VQLSs and alleviating optimization challenges in variational quantum algorithms.
Variational Quantum Linear Solvers (VQLS) are a promising method for solving linear systems on near-term quantum devices. However, their performance is often limited by barren plateaus and inefficient parameter initialization, which significantly hinder trainability as the system size increases. In this work, we introduce PVLS, a learning-based parameter prediction framework that uses Graph Neural Networks (GNNs) to generate high-quality initial parameters for VQLS circuits. By leveraging structural information from the coefficient matrix, PVLS predicts expressive and scalable initializations that improve convergence and reduce optimization difficulty. Extensive experiments on matrix sizes ranging from 16 to 1024 show that PVLS provides up to a 2.6x speedup in optimization and requires fewer iterations while maintaining comparable solution accuracy. These results demonstrate the potential of machine-learning-guided initialization strategies for improving the practicality of hybrid quantum-classical algorithms in the NISQ era.
The rapid evolution of Large Language Models (LLMs) has transformed natural language processing, enabling sophisticated applications across various sectors. However, the substantial computational demands associated with training and deploying LLMs result in significant energy consumption and carbon emissions. This study introduces an optimized hybrid quantum-classical framework that integrates variational quantum algorithms (VQAs) with accelerated classical learning techniques. By harnessing quantum computing for complex non-linear optimization and employing prompt learning to minimize full model retraining, the proposed approach enhances both computational efficiency and sustainability. Simulation outcomes indicate that the hybrid method can reduce energy usage by up to 30% and shorten computation time by 25% relative to conventional classical approaches, without diminishing model accuracy. These improvements are substantiated through quantitative analysis and visualized energy metrics. The adaptability of the framework supports its application in diverse areas, including sustainable energy management, supply chain optimization, and environmentally conscious transportation systems. Nevertheless, the broader implementation of such hybrid solutions remains constrained by current quantum hardware capabilities and integration challenges with classical infrastructure. The findings underscore the potential of hybrid quantum-classical optimization as a pathway toward sustainable AI development. Future research should prioritize advancements in quantum hardware reliability and interdisciplinary collaboration to accelerate practical adoption, thereby supporting global efforts in energy efficiency and environmental responsibility.