In order to solve the problem of non-ideal training sets (i.e., the
less-complete or over-complete sets) and implement one-iteration learning, a
novel efficient quantum perceptron algorithm based on unitary weights is
proposed, where the singular value decomposition of the total weight matrix
from the training set is calculated to make the weight matrix to be unitary.
The example validation of quantum gates {H, S, T, CNOT, Toffoli, Fredkin} shows
that our algorithm can accurately implement arbitrary quantum gates within one
iteration. The performance comparison between our algorithm and other quantum
perceptron algorithms demonstrates the advantages of our algorithm in terms of
applicability, accuracy, and availability. For further validating the
applicability of our algorithm, a quantum composite gate which consists of
several basic quantum gates is also illustrated.

提出了一种基于酉权重的高效量子感知器算法，通过计算来自训练集的总权重矩阵的奇异值分解，使权重矩阵达到酉性，并通过对量子门的示例验证证明该算法能够在一次迭代中精确实现任意量子门，与其他量子感知器算法的性能比较结果显示了该算法在适用性、准确性和可用性方面的优势，并且通过展示由多个基本量子门组成的量子复合门来进一步验证该算法的适用性。

一种基于单位权重的单次迭代量子感知器算法用于非理想训练集

A Unitary Weights Based One-Iteration Quantum Perceptron Algorithm for  Non-Ideal Training Sets

The quantum perceptron, the variational circuit, and the Grover algorithm
have been proposed as promising components for quantum machine learning. This
paper presents a new quantum perceptron that combines the quantum variational
circuit and the Grover algorithm. However, this does not guarantee that this
quantum variational perceptron with Grover's algorithm (QVPG) will have any
advantage over its quantum variational (QVP) and classical counterparts. Here,
we examine the performance of QVP and QVP-G by computing their loss function
and analyzing their accuracy on the classification task, then comparing these
two quantum models to the classical perceptron (CP). The results show that our
two quantum models are more efficient than CP, and our novel suggested model
QVP-G outperforms the QVP, demonstrating that the Grover can be applied to the
classification task and even makes the model more accurate, besides the
unstructured search problems.

本篇论文提出了一种新型的量子感知器 QVPG，它结合了量子变分电路和格勃算法，在分类任务中能够比传统感知器更高效地工作，并证明它比 QVP 更具优越性。

利用 Grover 算法模拟变分量子感知器

Simulation of a Variational Quantum Perceptron using Grover's Algorithm

We demonstrate that it is possible to implement a quantum perceptron with a
sigmoid activation function as an efficient, reversible many-body unitary
operation. When inserted in a neural network, the perceptron's response is
parameterized by the potential exerted by other neurons. We prove that such a
quantum neural network is a universal approximator of continuous functions,
with at least the same power as classical neural networks. While engineering
general perceptrons is a challenging control problem --also defined in this
work--, the ubiquitous sigmoid-response neuron can be implemented as a
quasi-adiabatic passage with an Ising model. In this construct, the scaling of
resources is favorable with respect to the total network size and is dominated
by the number of layers. We expect that our sigmoid perceptron will have
applications also in quantum sensing or variational estimation of many-body
Hamiltonians.

该研究论文证明了可以利用一个可逆的、多体的单元操作实现具有 Sigmoid 激活函数的量子感知器，并且在神经网络中插入该感知器可以构成一个连续函数的普适逼近器。这一构造中所需的资源随着网络总规模的变大而缩小，并主要由层数决定。最后，该研究还探讨了这种 Sigmoid 感知器在量子传感或多体哈密顿量变分估计方面的应用。