利用量子纠错学习任意 Lindbladian
Learning Arbitrary Lindbladians with Quantum Error Correction
- Harvard University（哈佛大学）
- ETH Zürich（苏黎世联邦理工学院）
- School of Engineering and Applied Sciences, Harvard University（哈佛工程学院与应用科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出首个无需预知结构的标准量子极限算法，通过递归随机稳定子码构造学习任意稀疏 Lindbladian，并在正则条件下实现哈密顿量的海森堡极限估计。
AI中文摘要：
我们研究无先验假设的 Lindbladian 学习问题，即在没有哈密顿量或耗散结构先验知识的情况下重建开放量子系统生成元。该问题呈现两种不同的信息论精度极限：未被耗散掩盖的哈密顿量分量受海森堡极限限制，而其余 Lindbladian 分量受二次方更差的标准量子极限限制。现有达到这些最优缩放的方法强烈依赖于预指定的相互作用和噪声结构，使得无先验假设的设置仍是开放问题。在这项工作中，我们提出了首个用于学习任意稀疏 Lindbladian 的标准量子极限算法。在额外的物理上合理的正则条件下，我们的框架还能在海森堡极限下学习与耗散部分不相交的哈密顿量分量，而无需预先知道哈密顿量或耗散支撑。我们的主要技术成分是递归随机稳定子码构造，该构造抑制最强的 Lindbladian 项，同时保持对较弱未知项的敏感性。这些结果建立了表征未知开放量子系统的可扩展框架，其中量子纠错作为关键学习原语。
英文摘要：
We study ansatz-free Lindbladian learning, the problem of reconstructing the generator of an open quantum system without prior knowledge of its Hamiltonian or dissipator structures. This problem exhibits two fundamental precision limits. Hamiltonian components not obscured by dissipation are Heisenberg-limited, while full Lindbladian reconstruction is subject to the quadratically worse standard quantum limit. This creates an apparent algorithmic impasse: achieving the Heisenberg-limited Hamiltonian learning requires suppressing unknown dissipation, which seemingly demands prior reconstruction of the noise and thereby incurs the standard-quantum-limit cost. In this work, we resolve this obstruction by giving an algorithm that learns the Hamiltonian disjoint from dissipator (HDD) at the Heisenberg limit without prior knowledge of either the Hamiltonian or dissipator supports. Our main technical ingredient is a randomized recursive stabilizer-code construction that progressively identifies and suppresses the dominant dissipative terms without reconstructing the full dissipator. Building on this framework, we also introduce an efficient end-to-end algorithm that learns the entire sparse Lindbladian at the standard quantum limit. Finally, we prove that in the ansatz-free setting, the HDD terms constitute the maximal set of Hamiltonian coefficients uniformly learnable at the Heisenberg limit. We show that every term outside HDD is fundamentally standard-quantum limited, extending prior no-go results to the ansatz-free setting. Together, our protocols provide a scalable framework for characterizing open quantum systems, with quantum error correction serving as a key learning primitive.
