Convolutional neural networks (CNNs) have rapidly risen in popularity for
many machine learning applications, particularly in the field of image
recognition. Much of the benefit generated from these networks comes from their
ability to extract features from the data in a hierarchical manner. These
features are extracted using various transformational layers, notably the
convolutional layer which gives the model its name. In this work, we introduce
a new type of transformational layer called a quantum convolution, or
quanvolutional layer. Quanvolutional layers operate on input data by locally
transforming the data using a number of random quantum circuits, in a way that
is similar to the transformations performed by random convolutional filter
layers. Provided these quantum transformations produce meaningful features for
classification purposes, then the overall algorithm could be quite useful for
near term quantum computing, because it requires small quantum circuits with
little to no error correction. In this work, we empirically evaluated the
potential benefit of these quantum transformations by comparing three types of
models built on the MNIST dataset: CNNs, quantum convolutional neural networks
(QNNs), and CNNs with additional non-linearities introduced. Our results showed
that the QNN models had both higher test set accuracy as well as faster
training compared to the purely classical CNNs.

本文介绍了一种新的变换层：quanvolutional layer，它可以通过在局部应用数个随机量子电路的方式对输入数据进行变换，类似于卷积过滤层。在 MNIST 数据集上的实验结果表明，用 QNN 可以比传统 CNN 享有更高的测试集精度和更快的训练速度。

量卷积神经网络：利用量子电路提升图像识别能力

Quanvolutional Neural Networks: Powering Image Recognition with Quantum  Circuits

A critical question for the field of quantum computing in the near future is
whether quantum devices without error correction can perform a well-defined
computational task beyond the capabilities of state-of-the-art classical
computers, achieving so-called quantum supremacy. We study the task of sampling
from the output distributions of (pseudo-)random quantum circuits, a natural
task for benchmarking quantum computers. Crucially, sampling this distribution
classically requires a direct numerical simulation of the circuit, with
computational cost exponential in the number of qubits. This requirement is
typical of chaotic systems. We extend previous results in computational
complexity to argue more formally that this sampling task must take exponential
time in a classical computer. We study the convergence to the chaotic regime
using extensive supercomputer simulations, modeling circuits with up to 42
qubits - the largest quantum circuits simulated to date for a computational
task that approaches quantum supremacy. We argue that while chaotic states are
extremely sensitive to errors, quantum supremacy can be achieved in the
near-term with approximately fifty superconducting qubits. We introduce cross
entropy as a useful benchmark of quantum circuits which approximates the
circuit fidelity. We show that the cross entropy can be efficiently measured
when circuit simulations are available. Beyond the classically tractable
regime, the cross entropy can be extrapolated and compared with theoretical
estimates of circuit fidelity to define a practical quantum supremacy test.

研究量子计算中的量子优越性，探讨基于（伪）随机量子电路输出分布的采样任务，指出在经典计算机上模拟需指数级时间，并在超级计算机模拟的基础上，得出了实现量子优越性所需的近 50 个超导量子位。引入交叉熵作为量子电路的评估标准，并提出基于交叉熵的量子优越性实验方案。