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arXiv 1805.03477quant-ph
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用于量子态鉴别的最优通用学习机

Optimal universal learning machines for quantum state discrimination

Marco Fanizza, Andrea Mari, Vittorio Giovannetti

备注：
15 pages without appendix (total 19), 5 figures, typos corrected, added plots, new results on the d-level system case, new noise simulations with QISKit Aer
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摘要：

我们考虑的问题是正确分类一个给定的量子二能级系统（量子比特），这是已知的两个同样可能的量子态之一。我们假设这个任务应该由一个量子机器来完成，它没有对两个模板态的完整经典描述，但只能有关于它们的纯度和相互重叠程度的部分先验信息。此外，类似于经典的监督学习范式，我们假设机器可以通过在第一模板状态下准备的$n$量子比特和在第二模板状态下准备的$n$更多量子比特来训练。在这种情况下，我们感兴趣的最佳过程，正确分类的输入量子比特与量子力学允许的最大概率。该问题的研究在其充分的一般性，为一些不同的先验信息的情况下，并为任意大小的$n$的训练数据。有限尺寸的渐近极限附近的修正$n\rightarrow \infty$也来自。当状态被假定为纯的，与已知的重叠，该问题也解决了d-能级系统的情况下。

英文摘要：

We consider the problem of correctly classifying a given quantum two-level system (qubit) which is known to be in one of two equally probable quantum states. We assume that this task should be performed by a quantum machine which does not have at its disposal a complete classical description of the two template states, but can only have partial prior information about their level of purity and mutual overlap. Moreover, similarly to the classical supervised learning paradigm, we assume that the machine can be trained by $n$ qubits prepared in the first template state and by $n$ more qubits prepared in the second template state. In this situation we are interested in the optimal process which correctly classifies the input qubit with the largest probability allowed by quantum mechanics. The problem is studied in its full generality for a number of different prior information scenarios and for an arbitrary size $n$ of the training data. Finite size corrections around the asymptotic limit $n\rightarrow \infty$ are also derived. When the states are assumed to be pure, with known overlap, the problem is also solved in the case of d-level systems.

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。

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