AI 中文总结
本研究提出元算法框架学习浅全对数量子电路，发现其在特定深度存在可学习性转变，结果对量子密码方案有启示意义。
AI 中文摘要
本工作考虑浅量子电路学习问题的一种变体：在给定对电路的查询权限及电路门布局知识的前提下，学习电路中使用的具体门，生成匹配该结构的操作等效电路。基于近期关于学习Haar随机砖墙电路的工作，我们提出一种元算法框架，用于学习基于电路前后端迭代局部门逆操作的广泛类别的电路。我们将这些技术应用于研究随机全对两局部电路，通过对光锥增长的分析，提供解析和数值证据表明，在大尺寸极限下，该集合在深度$d^* \sim \log_2 n + \log_2\log_2 n$处经历尖锐的可学习性转变。这些结果对近期提出的基于电路学习难度的量子密码方案具有启示意义，不过我们的设定存在重要差异，为未来研究提供了方向。
英文摘要
This work considers a variation on the problem of learning shallow quantum circuits. Given query access to the circuit, as well as knowledge of its gate layout, we consider the task of learning the specific gates used in the circuit, producing an operationally-equivalent circuit matching this structure. Building on recent work for learning Haar random brickwork circuits, we identify a meta-algorithmic framework for learning broad classes of circuits based on iterative local gate inversions at the front and back of the circuit. We apply these techniques to study random, all-to-all, two-local circuits, and provide analytical and numerical evidence that this ensemble undergoes a sharp learnability transition at depth $d^* \sim \log_2 n + \log_2\log_2 n$ in the large size limit, based on an analysis of lightcone growth. These results have implications for recently proposed quantum cryptographic schemes based on the difficulty of circuit learning, though there are important distinctions with respect to our setting that suggest avenues for future study.
Comments30 pages main body, 15 pages of appendices, 6 figures
