用于哈密顿学习和未知量子系统仿真的统一量子神经网络框架
Full-Trajectory Learning of Open Quantum Systems: Dynamical Emulation and the Limits of Hamiltonian Identifiability
- Department of Electrical and Electronics, Engineering Faculty, Ankara Yildirim Beyazit University（安卡拉耶尔德勒姆·拜亚泽特大学工程学院电气与电子工程系）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本研究提出基于QNN的框架，利用全密度矩阵轨迹学习实现黑盒哈密顿学习与量子系统仿真，通过合成数据集评估性能，可映射至物理架构并应用于量子数字孪生建模。
中文摘要 AI 辅助
准确识别未知量子系统对量子计算、传感和控制至关重要，因为哈密顿量（Hamiltonian）决定了量子态的演化。本研究提出一种基于量子神经网络（QNN）的框架，用于黑盒哈密顿学习和量子系统仿真，采用全密度矩阵轨迹学习方法。与仅基于最终状态或选定可观测量的方法不同，该方法利用了林德布拉德（Lindblad）动力学下密度矩阵的完整时间演化。生成符合物理规律的哈密顿量和耗散参数的合成数据集，以模拟实验测量结果。QNN学习从控制输入到32维哈密顿量系数向量的非线性映射，实现未知系统的重构和可微分仿真。引入啁啾激励（Chirped excitation）和随机初始量子状态以提升鲁棒性并提供更丰富的动力学信息。通过轨迹密度损失、量子态保真度和迹距离评估性能：随机初始化改善了态级重构，使单量子比特基准的保真度提升至0.929，未知系统的保真度提升至0.787，同时将迹距离分别降低至0.124和0.316；相比之下，啁啾激励主要通过加速收敛和降低轨迹密度损失来优化性能。最后，将学习到的哈密顿量映射到色散区的物理双量子比特总线谐振器架构，得到包括传输子（transmon）电容、约瑟夫森电感、量子比特间距及总线谐振器长度在内的关键电路参数。因此，该框架建立了从黑盒量子系统识别到物理量子仿真的数据驱动路径，在量子数字孪生建模中具有潜在应用。
英文摘要
Accurate identification of unknown quantum systems is essential for quantum computing, sensing, and control because the Hamiltonian governs quantum state evolution. This work proposes a QNN based framework for black box Hamiltonian learning and quantum system emulation using full density matrix trajectory learning. Unlike approaches based only on final states or selected observables, the method exploits the complete temporal evolution of the density matrix under Lindblad dynamics. A synthetic dataset of physically admissible Hamiltonians and dissipation parameters is generated to emulate experimental measurements. The QNN learns a nonlinear mapping from control inputs to a 32-dimensional Hamiltonian coefficient vector, enabling reconstruction and differentiable emulation of the unknown system. Chirped excitation and randomized initial quantum states are incorporated to improve robustness and provide richer dynamical information. Performance is evaluated using trajectory density loss, quantum-state fidelity, and trace distance. Randomized initialization improves state-level reconstruction, increasing fidelity to 0.929 for the single qubit benchmark and 0.787 for the unknown system, while reducing trace distance to 0.124 and 0.316, respectively. In contrast, chirped excitation primarily improves optimization by accelerating convergence and reducing trajectory density loss. Finally, the learned Hamiltonian is mapped onto a physical two qubit bus resonator architecture in the dispersive regime, yielding key circuit parameters including transmon capacitances, Josephson inductances, qubit separation, and bus-resonator length. The framework therefore establishes a data-driven pathway from black box quantum system identification to physical quantum emulation, with potential applications in quantum digital twin modeling.
