论文标题
使用量子信息瓶颈方法培训量子神经网络
Training quantum neural networks using the Quantum Information Bottleneck method
论文作者
论文摘要
我们在本文中提供了一种具体方法，用于培训量子神经网络，以最大程度地提高有关通过网络传输的属性的相关信息。这很重要，因为它给出了一个在操作上良好的数量，以优化训练自动编码器的输入和输出完全量子的问题。我们提供了一种严格的算法，用于计算错误$ o $ o（\ log^2（1/ε） + 1/δ^2）在错误$ε$内的量子信息瓶颈数量的价值，以查询输入密度操作员的纯化，如果其频谱在$上支持$ \ \ \ \ \ \ {0 \ forsup $ $ py $ \ y $ und $ und $ und $ undum和big and $ und $ und $ undud $和$ undum和big and \ big andududusuduseuseuse。相关密度矩阵的内核是不相交的。我们进一步提供算法来估计QIB函数的导数，表明可以使用QIB数量有效地训练量子神经网络，因为所需的梯度步骤的数量是多项式。
We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well founded quantity to optimize when training autoencoders for problems where the inputs and outputs are fully quantum. We provide a rigorous algorithm for computing the value of the quantum information bottleneck quantity within error $ε$ that requires $O(\log^2(1/ε) + 1/δ^2)$ queries to a purification of the input density operator if its spectrum is supported on $\{0\}~\bigcup ~[δ,1-δ]$ for $δ>0$ and the kernels of the relevant density matrices are disjoint. We further provide algorithms for estimating the derivatives of the QIB function, showing that quantum neural networks can be trained efficiently using the QIB quantity given that the number of gradient steps required is polynomial.
