执行NOT的k次根的量子和经典学习的速度
The speed of quantum and classical learning for performing the k-th root of NOT
摘要：
我们考虑量子学习机--为了以某种方式提高性能而修改自己的量子计算机--它们被训练来执行某些经典任务，即执行一个以经典位为输入并返回经典位作为输出的函数。这允许在完成学习所需的迭代次数方面对量子和经典学习机的学习效率进行公平比较。我们找到了一个明确的例子，数值模拟表明量子学习比经典学习更快。任务是提取NOT的第k个根（NOT =逻辑否定），其中k=2^m，m为\in N。这种加速的原因是经典机器需要大小为log k=m的内存来完成学习，而单个量子比特的内存对于任何k的量子机器来说都足够了。
英文摘要：
We consider quantum learning machines -- quantum computers that modify themselves in order to improve their performance in some way -- that are trained to perform certain classical task, i.e. to execute a function which takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machine in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the k-th root of NOT (NOT = logical negation), with k=2^m and m \in N. The reason for this speed-up is that classical machine requires memory of size log k=m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
