适用于多量子比特门合成的SU(N)上的迭代线性二次调节器
Iterative linear quadratic regulator on SU(N) for multi-qubit gate synthesis
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中文总结 AI 辅助
本研究将迭代线性二次调节器（iLQR）的李群公式适配到SU(N)并应用于多量子比特门合成，经对比验证其在不同场景下的收敛性能优势与特性。
中文摘要 AI 辅助
在量子最优控制理论中，基于梯度的轨迹优化技术已被证明在设计多量子比特量子门方面具有通用性。此外，融入 underlying 李群结构可加速优化过程。本研究将迭代线性二次调节器（iLQR）的李群公式适配到特殊幺正群SU(N)，并将其应用于量子门合成，在多个两至五量子比特门场景下与标准欧氏iLQR公式进行系统比较。研究发现，在理想化无约束设置中，所有李代数基元均可作为驱动哈密顿项，李群公式收敛速度快于欧氏iLQR公式；若驱动项被约束为两局域哈密顿项，李群变体在优化迭代初期收敛更快，但对初始化更敏感且更易陷入局部极小值。这些结果表明，将李群几何融入iLQR可显著提升收敛性，并凸显了约束控制设置下的重要改进方向。
英文摘要
In quantum optimal control theory, gradient-based trajectory optimization techniques have proven versatile in designing multi-qubit quantum gates. Furthermore, incorporating the underlying Lie-group structure can accelerate the optimization process. In this work, we adapt the Lie-group formulation of the iterative linear quadratic regulator (iLQR) to the special unitary group SU(N) and apply it to quantum gate synthesis, systematically comparing it against the standard Euclidean iLQR formulation across multiple two- to five-qubit gates. We find that in the idealized, unconstrained setting, where all Lie-algebra basis elements are available as drive Hamiltonian terms, the Lie-group formulation converges faster than the Euclidean iLQR formulation. If drive terms are constrained to 2-local Hamiltonian terms, the Lie-group variant converges faster in early optimization iterations, but exhibits greater sensitivity to initialization and a stronger tendency towards local minima. These results demonstrate that incorporating Lie-group geometry into iLQR substantially improves convergence and highlight important next steps for improvements in constrained control settings.
