Towards efficient numerical approaches for quantum control

Raj Chakrabarti, HERSCHEL A. RABITZ

Numerous lines of experimental, numerical and analytical evidence indicate that it is surprisingly easy to locate optimal controls steering quantum dynamical systems to desired objectives. This has enabled the control of complex quantum systems despite the expense of solving the Schrödinger equation in simulations and the complicating effects of environmental decoherence in the laboratory. Recent work indicates that this simplicity originates in universal properties of the solution sets to quantum control problems that are fundamentally different from their classical counterparts. Here, we review studies that aim to systematically characterize these properties, enabling the classification of quantum control mechanisms and the design of globally efficient quantum control algorithms.

André D. Bandrauk, Michel C. Delfour, Claude Le Bris

I. M. Korolev, Alexander Nikolaevich Pechen

In this work, we consider a formulation of the optimal gate generation problem for a fluxonium model of superconducting systems and apply it to the numerical analysis of the corresponding quantum control landscape in a vicinity of the null control. The model includes Schrödinger equation with control and maximization of the objective functionals for gate generation and observable mean value. For a qutrit fluxonium model, the third level can be considered as one of the three computational states. We exploit gradient of the control objective and GRAPE algorithm to perform numerical investigation of the quantum control landscapes for generation of the Hadamard, $$\mathrm{T}$$ , and $$\mathrm{S}$$ gates and for maximizing mean value of a quantum observable in a vicinity of the null control. The obtained results show high efficiency of gradient-based optimization when it starts from the null control and decrease of the efficiency with increase of the distance of the initial control from the null control for the gate generation problems, and an opposite behaviour for the mean value maximization. For gate generation, the obtained behavior differs (is opposite) from the behavior found previously for maximizing mean value of an observable for $$\Lambda$$ -type systems, that may indicate either the absence or low influence of trap at the null control for a fluxonium.

Uwe Sander

Alfio Borzı̀, Gabriele Ciaramella, M. Sprengel

Yusheng Zhao, Han Wang, Xin Liu +10 more

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.