arXiv 1802.060022018-02quant-ph

基于近期处理器的量子神经网络分类

Classification with Quantum Neural Networks on Near Term Processors

Edward Farhi, Hartmut Neven

备注：: 21 pages, 1 figure. Updated information in the acknowledgements

摘要：

我们介绍了一个量子神经网络，QNN，它可以表示标记的数据，经典或量子，并通过监督学习进行训练。该量子线路由一系列作用于输入量子态的依赖于参数的么正变换组成。对于二元分类，在指定的读出量子位上测量单个泡利算子。测量的输出是量子神经网络对输入状态的二进制标记的预测。首先，我们来看看分类经典的数据集组成的n位字符串与二进制标签。输入量子态是对应于样本串的n位计算基态。我们展示了如何设计一个由两个量子位幺正组成的电路，它可以正确地表示任何n位布尔函数的标签。对于某些标签功能的电路是指数长。我们引入了参数依赖酉，可以通过对标记数据的监督学习来适应。我们研究了一个例子，现实世界的数据组成的下采样图像的手写数字，其中每个已被标记为两个不同的数字之一。我们通过经典模拟表明，可以找到允许QNN学习正确区分两个数据集的参数。然后，我们将讨论将数据呈现为对应于不同标签值的计算基态的量子叠加。在这里，我们通过模拟来证明学习是可能的。我们考虑使用我们的QNN学习一般量子态的标签。通过例子，我们证明了这是可以做到的。我们的工作是探索性的，依赖于小量子系统的经典模拟。这里提出的QNN是在考虑到近期量子处理器的情况下设计的。因此，将有可能在短期门模型量子计算机上运行该QNN，其中可以探索其功率超出可以通过模拟探索的范围。

英文摘要：

We introduce a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning. The quantum circuit consists of a sequence of parameter dependent unitary transformations which acts on an input quantum state. For binary classification a single Pauli operator is measured on a designated readout qubit. The measured output is the quantum neural network's predictor of the binary label of the input state. First we look at classifying classical data sets which consist of n-bit strings with binary labels. The input quantum state is an n-bit computational basis state corresponding to a sample string. We show how to design a circuit made from two qubit unitaries that can correctly represent the label of any Boolean function of n bits. For certain label functions the circuit is exponentially long. We introduce parameter dependent unitaries that can be adapted by supervised learning of labeled data. We study an example of real world data consisting of downsampled images of handwritten digits each of which has been labeled as one of two distinct digits. We show through classical simulation that parameters can be found that allow the QNN to learn to correctly distinguish the two data sets. We then discuss presenting the data as quantum superpositions of computational basis states corresponding to different label values. Here we show through simulation that learning is possible. We consider using our QNN to learn the label of a general quantum state. By example we show that this can be done. Our work is exploratory and relies on the classical simulation of small quantum systems. The QNN proposed here was designed with near-term quantum processors in mind. Therefore it will be possible to run this QNN on a near term gate model quantum computer where its power can be explored beyond what can be explored with simulation.

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。

摘要：

英文摘要：

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