Shuang Cong

Shuang Cong, Fangfang Meng, Sen Kuang

The convergence of closed quantum systems in the degenerate cases to the desired target state by using the quantum Lyapunov control based on the average value of an imaginary mechanical quantity is studied. On the basis of the existing methods which can only ensure the single-control Hamiltonian systems converge toward a set, we design the control laws to make the multi-control Hamiltonian systems converge to the desired target state. The convergence of the control system is proved, and the convergence to the desired target state is analyzed. How to make these conditions of convergence to the target state to be satisfied is proved or analyzed. Finally, numerical simulations for a three level system in the degenrate case transfering form an initial eigenstate to a target superposition state are studied to verify the effectiveness of the proposed control method.

Shuang Cong, Fangfang Meng, Jianxiu Liu

A quantum system whose internal Hamiltonian is not strongly regular or/and control Hamiltonians are not full connected, are thought to be in the degenerate cases. In this paper, convergence problems of the multi-control Hamiltonians closed quantum systems in the degenerate cases are solved by introducing implicit function perturbations and choosing an implicit Lyapunov function based on the average value of an imaginary mechanical quantity. For the diagonal and non-diagonal tar-get states, respectively, control laws are designed. The convergence of the control system is proved, and an explicit design principle of the imaginary mechanical quantity is proposed. By using the proposed method, the multi-control Hamiltonians closed quantum systems in the degenerate cases can converge from any initial state to an arbitrary target state unitarily equivalent to the initial state. Finally, numerical simulations are studied to verify the effectiveness of the proposed control method.

Chenyu Su, Weiwei Shang, Chen Qian et al.

Semantics-driven 3D spatial constraints align highlevel semantic representations with low-level action spaces, facilitating the unification of task understanding and execution in robotic manipulation. The synergistic reasoning of Multimodal Large Language Models (MLLMs) and Vision Foundation Models (VFMs) enables cross-modal 3D spatial constraint construction. Nevertheless, existing methods have three key limitations: (1) coarse semantic granularity in constraint modeling, (2) lack of real-time closed-loop planning, (3) compromised robustness in semantically diverse environments. To address these challenges, we propose ReSem3D, a unified manipulation framework for semantically diverse environments, leveraging the synergy between VFMs and MLLMs to achieve fine-grained visual grounding and dynamically constructs hierarchical 3D spatial constraints for real-time manipulation. Specifically, the framework is driven by hierarchical recursive reasoning in MLLMs, which interact with VFMs to automatically construct 3D spatial constraints from natural language instructions and RGB-D observations in two stages: part-level extraction and region-level refinement. Subsequently, these constraints are encoded as real-time optimization objectives in joint space, enabling reactive behavior to dynamic disturbances. Extensive simulation and real-world experiments are conducted in semantically rich household and sparse chemical lab environments. The results demonstrate that ReSem3D performs diverse manipulation tasks under zero-shot conditions, exhibiting strong adaptability and generalization. Code and videos are available at https://github.com/scy-v/ReSem3D and https://resem3d.github.io.