3D Scalable Quantum Convolutional Neural Networks for Point Cloud Data Processing in Classiﬁcation Applications

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3D Scalable Quantum Convolutional Neural

Networks for Point Cloud Data Processing in

Classiﬁcation Applications

Hankyul Baek, Won Joon Yun, and Joongheon Kim

Department of Electrical and Computer Engineering, Korea University, Seoul 02841, Republic of Korea

67back@korea.ac.kr,ywjoon95@korea.ac.kr,joongheon@korea.ac.kr

Abstract—With the beginning of the noisy intermediate-scale

quantum (NISQ) era, a quantum neural network (QNN) has

recently emerged as a solution for several speciﬁc problems that

classical neural networks cannot solve. Moreover, a quantum

convolutional neural network (QCNN) is the quantum-version

of CNN because it can process high-dimensional vector inputs

in contrast to QNN. However, due to the nature of quantum

computing, it is difﬁcult to scale up the QCNN to extract a

sufﬁcient number of features due to barren plateaus. Motivated

by this, a novel 3D scalable QCNN (sQCNN-3D) is proposed

for point cloud data processing in classiﬁcation applications.

Furthermore, reverse ﬁdelity training (RF-Train) is additionally

considered on top of sQCNN-3D for diversifying features with

a limited number of qubits using the ﬁdelity of quantum

computing. Our data-intensive performance evaluation veriﬁes

that the proposed algorithm achieves desired performance.

Index Terms—Point Cloud Classiﬁcation, Quantum Convolu-

tional Neural Networks, Quantum Machine Learning.

I. INTRODUCTION

A point cloud is expected to be desirable three-dimensional

sensory data and it is widely and actively used in various

ﬁelds, including robotics [1] and autonomous vehicles [2]–[4].

In addition, the point clouds are alternative data to precisely

analyze and rebuild our surrounding real-world situations [5].

Currently, millions of point cloud vertices per second can be

produced by laser imaging detection and ranging (LiDAR)

sensors. Furthermore, according to Global Market Insights

[6], the market size of point cloud processing related media

services will reach more than 15 billion dollars in 2030.

Spurred by the advance of LiDAR, recent studies on point

cloud processing have shown that neural network (NN) can

be an alternative solution for various tasks such as classiﬁ-

cation [7], object detection [8], [9], and segmentation [10].

However, due to abundant spatial geometric information and

the massive size of the point cloud, operating the point cloud

processing is still challenging [11]. A point cloud usually has

around 100k vertices, and each vertex consists of a lot of

information, i.e., color and Cartesian coordinates. Therefore,

classical computing methodologies are obviously harsh to

utilize the point cloud in real-time and even jammed when

they utilize NN.

Quantum computing can be a reasonable solution to these

challenges. The quantum computing utilizes a quantum bit

(qubit), the counterpart in quantum computing to the binary

bit of classical computing. Due to the characteristic of qubit

that ranges from 0to 1, not exact integer 0or 1in classical

computing, quantum computing can enlarge its computation

capability on an exponential scale [12]–[15]. In addition, par-

allelization is one of the beauty of quantum computing. Thus,

quantum algorithms have shown that they are able to solve

several NP-hard problems in polynomial time, such as Shor

algorithm [16] and Grover search algorithm [17], those are

physically impossible in classical approaches [18]. Therefore,

quantum computing can outperform classical algorithms in

terms of processing speed for some problems under speciﬁc

conditions [19], [20].

In this paper, we focus on grafting quantum machine

learning (QML) methodologies to point cloud data processing

which requires tremendous computational costs [21]. In na¨

ıve

and straightforward approach to process point cloud data,

increasing the number of qubits or gates can be intuitively

considered. However, the trainability issue occurs because the

number of local minima (i.e., barren plateau) is proportion to

the exponential number of gates in QNN [22]. Therefore, this

approach is not considerable. Fortunately, it has been proven

that the barren plateaus can be eliminated in quantum con-

volutional neural network (QCNN) [23]. Furthermore, image

processing with QCNN shows better feasibility when QCNN is

used together with classical NN, i.e., fully connected network

(FCN) [24], which can be called a quantum-classical hybrid

classiﬁer. It has been experimentally proven that hybrid QML

achieves considerable performance in classiﬁcation tasks [25].

Thus, it is better to use hybrid QCNNs in point cloud process-

ing applications.

On top of these current research progresses, there still

remain important questions on QCNN methodologies, i.e., (i)

how to upload tremendous classical data into QCNN?,(ii)

how to train QCNN efﬁciently?, and (iii) how to make the

complexity of QCNN be proportioned to performance? In order

to answer these questions, we aim to extend a 3D voxelized

version of scalable QCNN under the consideration of barren

plateaus, data uploading issues, and efﬁcient training methods.

First of all, we propose a 3D voxelized version of scalable

QCNN, i.e., 3D scalable QCNN (sQCNN-3D). Moreover, we

alleviate the data uploading issue by adopting data-reuploading

[26]. Furthermore, a new scaling strategy is proposed for

leveraging the various sizes of quantum convolutional ﬁlters.

arXiv:2210.09728v1 [quant-ph] 18 Oct 2022

Finally, in order to realize efﬁcient training, we propose a

3-dimensional reverse ﬁdelity-train (3D RF-Train), which let

sQCNN-3D fully utilize the point cloud’s intrinsic features

while utilizing only a limited number of qubits. Our proposed

methods can not only resolve the aforementioned challenges

but also answer the questions mentioned above.

Contributions. The major contributions of the research results

in this paper can be categorized as follows.

•First of all, a novel scalable QCNN architecture for

extensible 3D data processing, i.e., sQCNN-3D, in order

to achieve scalability while pursuing quantum supremacy

and also avoiding barren plateaus.

•Moreover, an additional sQCNN-speciﬁc training algo-

rithm, i.e., RF-Train, in order to extract the intrinsic

features with a ﬁnite number of qubits.

•Furthermore, a new scaling strategy is also proposed

which unleashes the potential of sQCNN-3D. More ﬁlters

are corroborated in order to induce higher accuracy.

•Lastly, data-intensive experiments are conducted to cor-

roborate the superiority of sQCNN with RF-Train, in

ModelNet and ShapeNet, widely used in the literature.

Organization. The rest of this paper is organized as follows.

Sec. II brieﬂy introduces the differences between CNN and

QCNN; and the concept of quanvolution. Sec. III presents

our proposed 3D scalable QCNN for point cloud processing

in classiﬁcation. Sec. IV evaluates the performance of the

proposed algorithm. Lastly, Sec. V concludes this paper.

II. PRELIMINARIES

A. Point Cloud Processing with Classical CNN

There are two main categories in point cloud process-

ing, i.e., point-wise processing [27] and voxel-based process-

ing [28], [29], and the later one is the major trend in the

literature. A classical CNN for the voxel-based processing

is mainly composed of four procedures, i.e., embedding,

convolution, pooling, and prediction.

Embedding. In contrast to a 2D image, each point cloud in 3D

data has a huge number of vertices. Thus, a set of vertices in

each point cloud is embedded as features to reduce the com-

putational complexity as well as improve the robustness for

perturbation. PointGrid [30] embeds each set of vertices into

voxel grids to achieve sophisticated local geometric features;

and DGCNN [31] extracts edge features from a set of vertices

to incorporate local neighborhood information.

Convolution. After embedding the high dimensional point

cloud data into features, the features can be convoluted by a

set of ﬁlters. With trainable parameters, ﬁlters slid across each

axis of features, i.e., named input features. The dot products

between the input features and ﬁlters are computed at every

spatial position.

Pooling. This pooling computation is conducted to reduce

the dimension of the convolved input features. This is usu-

ally considered as a critical part of point cloud CNN-based

models because it speeds up the subsequent convolution layer

computation [32]. In addition, it allows these models to learn

representations invariant to minor translations.

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|0⟩

!!𝑈(𝑭𝒘,𝒉,𝒅%)

𝑈(𝑭𝒘,𝒉&𝟏,𝒅%)

𝑈(𝑭𝒘,𝒉&𝟏,𝒅&𝟏%)

𝑈(𝑭𝒘&𝟏,𝒉&𝟏,𝒅%)

!!𝑈(𝑭𝒘,𝒉,𝒅&𝟏)

𝑈(𝑭𝒘&𝟏,𝒉,𝒅%)

𝑈(𝑭𝒘&𝟏,𝒉,𝒅&𝟏%)

𝑈(𝑭𝒘&𝟏,𝒉&𝟏,𝒅&𝟏)

!!𝑈(𝜃)

Input Embeded Feature

𝑈(𝑭𝒘:𝒘#𝟐,&𝒉:𝒉#𝟐,&𝒅:𝒅#𝟐)

Fig. 1. An illustration of multi-qubit reuploading in sQCNN-3D (q=4, κ=2).

Prediction. For the prediction, the fully connected layers

receive feature information which is derived from convolution

layers and pooling layers. According to the universal approx-

imation theorem [33], fully connected layers are allowed to

make a prediction. By optimizing the objective function (e.g.,

cross-entropy loss or mean-squared error loss), conventional

classical CNN can achieve the prediction to the desired classes.

B. Quantum CNN

QCNN is the quantum version of CNN, which leverages a

parameterized quantum circuit (PQC) as convolutional ﬁlters.

With the QCNN which utilizes quanvolutional ﬁlters [34],

spatial information can be exploited with particular character-

istics. Note the deﬁnition of quanvolution is explained later.

Basic Quantum Operation. All quantum-related notations

and their operations are represented as Dirac-notation. In

contrast to classical computing, a qubit can have two pos-

sible states denoted as |0iand |1i[35]. The quantum state

in an q-qubit system is deﬁned as 2qpossible bases and

their probability amplitudes, i.e., |ψi,P2q

k=1 αk|kiwhere

|kidenotes a basis in Hilbert space, ∀q∈N[1,∞)and

P2q

k=1 |αk|2= 1. The operation of quantum state |ψiis

represented with unitary matrix U, and its operation is ex-

pressed as |ψi ← U· |ψi. Note that the quantum state is not

deterministic. Therefore, the quantum state is transformed into

classical data only with its measurement; and the measurement

of the quantum state is represented as a set of projection

matrices M,{Mk}q

k=1. This paper uses the measurement

matrix Mk=I⊗k−1⊗Z⊗I⊗q−k,∀k∈[1, q], where I

denotes the identity matrix and Z=1 0

0−1. Then, the

classical output (called observable) is obtained as follows,

hOki=hψ|Mk|ψi. Here, the measurement is an activation

function. In other words, the unitary matrix and measurement

operation are mapped to linear operation and activation func-

tion, respectively, which leads to QML feasible [36].

Quanvolution. The quanvolutional ﬁlter is deﬁned to fol-

low the two consecutive procedures, i.e., (i) data encoding-

processing and (ii) measurement.

1) Data Encoding-Processing: To use quanvolutional ﬁlter

with classical data, the encoding strategy should be con-

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3DScalableQuantumConvolutionalNeuralNetworksforPointCloudDataProcessinginClassicationApplicationsHankyulBaek,WonJoonYun,andJoongheonKimDepartmentofElectricalandComputerEngineering,KoreaUniversity,Seoul02841,RepublicofKorea67back@korea.ac.kr,ywjoon95@korea.ac.kr,joongheon@korea.ac.krAbstractWiththe...

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3D Scalable Quantum Convolutional Neural Networks for Point Cloud Data Processing in Classiﬁcation Applications

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