论文标题
布尔功能的可调量子神经网络
Tunable Quantum Neural Networks for Boolean Functions
论文作者
论文摘要
在本文中，我们提出了一种新的量子神经网络的方法。我们的多层体系结构避免使用通常模拟经典神经网络特征的非线性激活函数的测量。尽管如此，我们提出的架构仍然能够学习任何布尔功能。这种能力来自布尔函数和由多控制的不门制成的特定量子电路之间存在的对应关系。该对应关系是通过称为代数正常形式的函数的多项式表示构建的。我们使用这种结构来介绍通用量子电路的想法，该量子电路可以调整大门以学习任何布尔功能。为了执行学习任务，我们设计了一种利用没有测量的算法。当呈现所有长度$ n $的二进制输入的叠加时，网络最多可以在$ n+1 $更新中学习目标功能。
In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural networks. Despite this, our proposed architecture is still able to learn any Boolean function. This ability arises from the correspondence that exists between a Boolean function and a particular quantum circuit made out of multi-controlled NOT gates. This correspondence is built via a polynomial representation of the function called the algebraic normal form. We use this construction to introduce the idea of a generic quantum circuit whose gates can be tuned to learn any Boolean functions. In order to perform the learning task, we have devised an algorithm that leverages the absence of measurements. When presented with a superposition of all the binary inputs of length $n$, the network can learn the target function in at most $n+1$ updates.
