Clifford 随机化乘积态的高效学习
Efficient Learning of Clifford-Scrambled Product States
- Quantum Research Center, Technology Innovation Institute（量子研究中心，技术创新研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出从两拷贝 Bell 采样中高效学习 Clifford 随机化乘积态的方法，通过二次关系和二元线性代数构造解纠缠器，实现 O(n^2) 样本学习及 T 深度一电路的精确学习，并排除相关伪随机态。
AI中文摘要：
作用于乘积魔法态的 Clifford 电路提供了一种紧凑的 ansatz，展现出广泛的魔法性、体积律纠缠，甚至在标准复杂性假设下具有经典难以采样的特性。在此，我们从两拷贝 Bell 采样中高效恢复其隐藏的乘积子系统。Bell 样本之间的二次关系在去除 Pauli 稳定子后决定不可约块，而二元线性代数构造了一个 Clifford 解纠缠器。对于对数大小的块，只要状态保持与获得额外 Pauli 稳定子的逆多项式分离，完整状态的近似学习就是高效的。我们通过 O(n^2) 个 Bell 样本高效学习由随机 T 掺杂 Clifford 电路制备的 n 量子比特状态，其中 T 门密度低于一，并在 Clifford 增强的矩阵乘积态中解纠缠隐藏的乘积块。对于酉学习，我们使用 O(n^2) 次查询精确学习 T 深度为一的电路。最后，我们排除了由 Clifford 电路隐藏的具有乘积二分区的伪随机状态和酉。
英文摘要：
Clifford circuits acting on product magic states provide a compact ansatz exhibiting extensive magic, volume-law entanglement, and even classically hard sampling under standard complexity assumptions. Here, we efficiently recover its hidden product subsystems from two-copy Bell sampling. Quadratic relations between Bell samples determine the irreducible blocks after removing Pauli stabilizers, and binary linear algebra constructs a Clifford disentangler. For logarithmic-size blocks, approximate learning of the full state is efficient whenever the state remains inverse-polynomially separated from acquiring additional Pauli stabilizers. We efficiently learn $n$-qubit states prepared by random $T$-doped Clifford circuits with $T$-gate density below one via $O(n^2)$ Bell samples, and disentangle hidden product blocks in Clifford-augmented matrix product states. For unitary learning, we exactly learn $T$-depth-one circuits using $O(n^2)$ queries. Finally, we rule out pseudorandom states and unitaries with a product bipartition hidden by Clifford circuits.
