通过测量与反馈实现的态制备：推引关系、态结构及非可逆对称性
State preparation via measurement and feedback: pushing relations, state structures, and non-invertible symmetries
浏览论文内容
中文总结 AI 辅助
该研究提出基于可推引缺陷的方案，通过测量与反馈线路实现一维量子态制备，揭示了此类线路与非可逆对称性的内在联系。
中文摘要 AI 辅助
带有测量和幺正反馈（MF）的量子线路可在常数深度下制备长程纠缠态，但针对给定目标态的MF制备线路的系统构建方法仍有待深入探索。我们基于可推引缺陷的概念为一维态开发了此类方案：矩阵乘积态的虚拟键算子可通过张量推引，代价是引入一个物理反馈幺正变换。我们证明，可推引缺陷集合及其推引关系可对有限深度MF可制备态进行分类，并决定其制备线路。对每类目标态|A〉，我们关联一个态|B〉，使得|A〉可通过一轮MF线路制备；特别地，当|B〉可由有限深度局域幺正（FDLU）线路制备时，|A〉可从乘积态出发，通过含一轮MF的线路制备。对一般目标态，该方案通过迭代此过程直至关联态可由FDLU制备得到。对于开边界矩阵乘积态，该方案是完备的：只要带左条件反馈修正的有限深度MF制备可行，它就能构造出对应的制备线路。因此，可推引缺陷与推引关系成为通过测量与反馈实现量子态制备的统一原理。该表征进一步揭示了MF线路与非可逆对称性之间的内在联系：具有特定类推引关系的态与乘积态通过Tambara-Yamagami对偶算子、或带有融合规则L_α L_α' = L_{α+α'} + L_{α-α'}的连续余弦对称性算子及其推广（直至非横向门）相关联。
英文摘要
Quantum circuits with measurements and unitary feedback (MF) can prepare long-range entangled states in constant depth, but a systematic construction of the MF preparation circuit for a given target state remains underexplored. We develop such a scheme for one-dimensional states, based on the notion of pushable defects: virtual-bond operators of a matrix product state that can be pushed through the tensor at the price of a physical feedback unitary. We show that the set of pushable defects, together with their pushing relations classifies finite-depth MF-preparable states and dictates their preparation circuits. To each class of the target state $|A\rangle$, we associate a state $|B\rangle$ from which $|A\rangle$ can be prepared using a 1-round MF circuit; in particular, $|A\rangle$ is preparable from a product state using a circuit with 1 round of MF whenever $|B\rangle$ is preparable by a finite-depth local unitary (FDLU) circuit. For a general target state, the scheme is obtained by iterating this procedure until the associated state is FDLU-preparable. For open-boundary matrix product states, the scheme is complete: it constructs a preparation circuit whenever finite-depth MF preparation with left-conditioned feedback corrections is possible. Pushable defects and pushing relations thus emerge as a unifying principle for quantum state preparation via measurements and feedback. This characterization further reveals an intrinsic connection between MF circuits and non-invertible symmetries: states with certain classes of pushing relations are related to a product state by Tambara-Yamagami duality operators, or by continuous cosine symmetry operators with fusion rules $L_α L_{α'} = L_{α+α'} + L_{α-α'}$, together with their generalizations up to (not necessarily transversal) gates.
