Remote Sensing Image Scene Classification in Hybrid Classical-Quantum Transferring CNN with Small Samples

1. Introduction

In recent times with the rocketing progress of the earth observation capability and the intelligent computing technology, the progression and innovation of remote sensing(RS) is more important than ever. RS image data processing is now developing towards RS Big Data Era, which relies on data model by data-driven intelligent analysis [1]. Machine learning(ML) plays an essential role in extracting underlying features or a probability distribution of patterns in RSI datasets, such as trend prediction, target recognition, change detection, or image classification in hitherto unknown domains [2]. In particular, deep learning (DL) has proven to be a technological innovation and a historic milestone in many fields [3]. It emphasizes neural networks (NNs) involving multiple hidden layers, which use feature representations learned exclusively from the data, instead of handcrafted features that are designed based mainly on domain-specific knowledge. DL has widely used in various research topics, for example data analysis tasks, including semantic segmentation, image classification, target detection, scene classification, change detection and three-dimensional reconstruction.

Deep learning algorithms has opened up an entirely novel frontier of learning algorithms including CNNs techniques that have been adopted in the RS image recognition and image classification [6]. Various deep learning models have been developed with outstanding performance for RSISC on RSI datasets in multiple applications [8–10]. But the CNN architecture construction requires skill in both DL methodology and professional expertise [11], the efficiency of CNN models remains a huge challenge. CNNs can extract hierarchical and insightful features automatically from massive size of image data [7]. Early studies involving RSISC in CNN were transplanted from natural image data, which led to increase the difficulty of RSISC task in complex RSIs [4], and handmade architecture design is troublesome and fallible, experienced and mature professionals in both DL and the investigated domain are often not available in practical applications. Since then, researchers have aimed to replace hand-engineered features with trainable multilayer networks, so enhancement capability of feature representation has become the main research technique [5].

Most studies on CNN-based RSISC have used pre-trained CNN models as features extractors to extract high semantic features. Researchers have utilized networks that are pre-trained on different networks, for instance AlexNet [12], VGGNet [13], GoogleNet [14], and ResNet [15], stand out among numerous DL-based methods due to closely related powerful features extraction performance. Although both assignments involve RSIs data and the pre-trained networks can easily be operated for transferring in RSISC, these methods have limitation: It has no advantage if significant domain differences exist between source and target datasets. Furthermore RSIs differ significantly in terms of spectral resolutions, spatial resolution, and radiometric resolution etc.[16].

Fine-tuning CNN-based models is an effective tool for RSISC. However, such approaches still have limitations in three perspectives related to datasets, models, and labels. These limitations are discussed below.

Firstly, the dataset plays a important role in advancing RSISC. The Size-Similarity Matrix of dataset determines the choices of the pre-trained model. This matrix classifies the strategies based on the size of the dataset and its similarity to the dataset in which the pre-trained model was trained. Due to the matrix transformation conducted in the fully connected layers, the dataset must be transformed into a certained fixed size. The most common approach is to crop and interpolate the original image, which inevitably results in a loss of fine information from the original RSIs. Unfortunately, either of these approaches can be detrimental to the performance of RSISI. Therefore, the selection of the pre-trained models depends on the dataset's size and size-similarity. The RSIs dataset must be transformed into a special fixed size [17].

Secondly, from a modeling perspective, most pre-trained models can achieve excellent classification performance. However, these models also have some limitations. The learned feature may be not entirely satisfactory for the properties of targets datasets and per-trained treatments applied between heterogeneous networks require manual manipulations of layer combinations, depending on type of task. The RSISC task, in particular, requires a massive tuning procedure to achieve optimal classification performance.

Thirdly, many scene images with same exteriors have different but correlated scene categories, which can lead to the label paradox. Because a RSI contains various objects, such as water, mountains, nudation and buildings etc, which may be covered in a residential scene as shown in Figure 1. The variance and complex spatial distributions of ground objects cause the diversity of RSISC. As a result of the different varieties in the exteriors of ground objects within the similar semantic information, traditional methods of RSISC often fail to achieve satisfactory classification accuracy due to low sort separability caused by the presence of the same objects within different scene sorts or the high semantic superimposed between different scene categories. Another important difficulty of RSISC is the large variance of object scales caused by sensor imaging altitude variation. Furthermore, the label distribution of ground objects in dataset is often unavailable in original training dataset and needs to be modeled label paradox, which is typically caused by resembling sample dataset that have different but correlated labels, as can be seen in Figure 1 [18].

Quantum computing are emergent techniques that have the potential to transform the research and application of remote sensing. Quantum computing can provide significant advantages in terms of improving the performance of classification techniques. The great potential of quantum computing in ML has been actively investigated. In specific cases, traditional machine learning tasks can be improved with exponential speedups when it operates on a quantum computer [21,22]. The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum computing that has been successfully implanted in conventional ML theories and topics, such as data mining, artificial neural networks, computational learning theory, etc., as shown in [23,24,25,26,27]. HHL-based algorithms is based on the quantum phase estimation algorithm, which operates in a high depth quantum circuit [28]. To bypass this strict requirement of hardware, classical-quantum hybrid algorithms containing a low depth quantum circuit for instance the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) have been suggested [29,30]. The idea of a hybrid algorithm is to divide the problem into two components, either of which can be operated on a quantum and a classical computer separately. Cai verified the feasibility of K-Means algorithm on a quantum computer [31]. Otgonbaatar proposed a parameterized quantum circuit (PQC) with only 17 quantum bits for classifying a two-label Sentinel RSI dataset. A quantum-based pseudo-labelling for hyperspectral imagery classification is demonstrated by R. U. Shaik. Noisy intermediate-scale quantum (NISQ) devices are a advanced quantum computing technology providing solutions for large-scale and complex practical quantum computation, such as solving high-complexity problems or supporting ML algorithms. An NISQ device is termed a variational quantum circuit (VQC) when it has parameterized quantum gates and parameterized quantum circuit. Sometimes, the VQC is a supervised learning algorithm in which quantum neural networks (QNNs) are trained to perform a classification mission. The transfer learning approach in the quantum domain has been largely unexplored, with only very little applications such as modeling quantum many-body system (MBS), associated with classical autoencoders to a quantum Boltzmann machine, and initializing variational quantum networks. In the paper, a innovative, self-designed and systematic theory through a concept of tensor quantum circuits and pre-trained networks is proposed.

Our study demonstrate that hybrid classical-quantum transferring CNN models can significantly enhance the efficient and performance of RSISC with small training samples and investigate the feasibility of the hybrid classical-quantum(CQ) transferring CNN model for RSISC. In this paper, we focus on the hybrid models scenario and proposed an improved hybrid classical-quantum(CQ) transfer learning CNNs composed of classical and quantum elements that can extract high informative feature efficiently with a VQC.

The remaining sections of this work are introduced as follows: Section 2 introduces some notations about hybrid classical-quantum networks. Section 3 outlines the architecture of the hybrid classical-quantum transferring CNN. Section 4 reports the evaluation an results of our model. Finally, the paper is concluded in Section 5.

2. Hybrid Classical-Quantum Networks

2.1. Vairiational Quantum Circuits

VQCs usually can define a subcircuit, which is a basic circuit architecture where complex VQCs can be constructed through repeating layers. Circuits consists of multiple rotating logic gates as well as CNOT logic gates that entangle each qubit with its neighbouring qubit. We also need a line to encode the classical data onto the quantum state, so that the output of the line measurement is related to the input. In this case, we encode the binary input onto the qubits of the corresponding order.

VQC can define a quantum layer similar to the classical neural network. Furthermore, arbitrary VQC U can be demonstrated

$$\mathcal{L}=U\left(\mathrm{w}\right)|x⟩$$

(1)

where w denotes variational parameters, a unitary operation is realized acting on the input state |x〉of n_q quantum subsystems.

The depth d of a VQC is a superposition of different quantum circuits and match the product of various parameterized unitaries with different weights:

$$\mathcal{L}={\mathcal{L}}_d\circ ...{\mathcal{L}}_2\circ {\mathcal{L}}_1$$

(2)

The first step is transformation of the classical image dataset into quantum state, the process denotes quantum state coding (QSE). This operation can be realized through a variational circuits depending on x. Single-qubit rotations or single mode displaces parameter x. And the quantum layer ε maps classical vector space into Hilbert space.

On other hand, for extraction of a classical output y we can measure the expectation values of n_q local obervables ẑ=[ẑ₁,ẑ₂,...ẑ_n]. The process is known as a measurement layer, which maps a quantum state to a classical dataset.:

$$\mathsf{{\rm M}}:=⟨x|\widehat{z}|x⟩$$

(3)

The initial quantum layers and the final measurement state in the quantum circuits can be globally written as follows

Q = M∘L∘ε

(4)

2.2. Tensor Quantum Circuits

The VQC algorithm is limited to parameters adjustment, using the quantum computer as feedback circuits to adjust the parameters in the parameterized circuits to optimal values. It can only optimize the structure of the fixed circuit, cannot change its own structure, nor increase the number of entanglement operations or change the entanglement characteristics expressed, so the algorithm still means the quantum chip entanglement operation. For complex Hamiltonian, such as correlated systems, this common method performs not well.

Tensor quantum circuits adopt the classical quantum hybrid algorithm.The classical part adopts the form of tensor network to process the higher order tensor into the form of multiple lower order tensor compressors. The quantum part adopts VQC to adjust the parameters. Tensor quantum circuits consist of n qubits, and consisting of k layers. Parameterized e^iθX⊗X gates are between each neighboring qubit in each layer, then followed by a series of single-qubit parameterized Z and X rotations..

Figure 2. An illustration of tensor quantum circuits.

Figure 2. An illustration of tensor quantum circuits.

3. Hybrid Classical-Quantum Transferring CNN

In the following section we introduce the concept of transferring prior “knowledge” from classical to quantum. A hybrid classical-quantum transferring CNN for RSISC proposal on the basis of two networks A and B is defined in Figure 3.

A hybrid classical-quantum transferring CNN for RSISC proposal (as shown in Figure 3.) A pre-trained network A on a dataset D_A for a task C_A is CNN’. Then the final layers are removed. The reduced network A’ can be taken as feature extractor. A new trainable network B can integrate closely the pre-trained network A’. The parameters of network B can adjust finely on the specific dataset.

D_A=ImageNet：ImageNet Large Sclae Visual Recognition Challenge (ILSRC) with many classes [32].

A = ResNet34: a pre-trained residual neural network [33].

C_A =Image Classification .

A’= ResNet34 a residual neural network without the final layer.

D_B = RSI datasets

B = Q = L_4→2ºQºL_512→4 :i.e., 4-qubit tensor quantum circuits and outputs.

C_B = RSISC.

The strategy of feature extraction is much more general than what we needed in this work. In the context for transfer learning, the reduced pre-trained network A’ is interpretered as a feature extractor, after removing the final layer of A. A’ can produce features that are not problem-specific. In hybrid structure, the network A is classical and the network B is quantum.

Nowadays classical hybrid transfer learning is perhaps the definitely efficient and mature tools of DL in the current technological era of ML. It is commonly validated as the successful ML algorithms, especially for RSISC.

The quantum circuits model in Equation (5) demonstrates the concept. We assume quantum circuits of 4 qubits and utilize the following model:

$$\tilde{Q}=L_{4\to 2}\circ Q\circ L_{2\to 4}$$

(5)

where L_2→4 implies residual networks using the activation function tanh φ = tanh, Q is VQC, and L_4→2 denotes residual networks without activation function. The strategy of quantum encoding establishes linkages between the image dataset input x and its quantum state |x〉. The chosen embedding map from the classical image dataset input vector can be written as Equation (7)：

$$\epsilon \left(x\right)={⨂}_{i=1}^4\left(R_y\left(\pi x_i\right)\mathrm{H}\right){|0⟩}^{⨂4}=\left[\begin{array}{c}cos\left(\pi x_1\right)\\ sin\left(\pi x_1\right)\end{array}\right]⨂\left[\begin{array}{c}cos\left(\pi x_2\right)\\ sin\left(\pi x_2\right)\end{array}\right]⨂\left[\begin{array}{c}cos\left(\pi x_3\right)\\ sin\left(\pi x_3\right)\end{array}\right]⨂\left[\begin{array}{c}cos\left(\pi x_4\right)\\ sin\left(\pi x_4\right)\end{array}\right]$$

(6)

$$L\left(x\right):|x⟩\to |y⟩={K⨂}_{i=1}^4{R}_y\left(\pi x_i\right)|x⟩$$

(7)

where H denotes a single Hadamard gate. The quantum circuits consists of 4 variational circuits. And K indicates an entangling unitary operation of 3 CNOT gates. The model in the red frame demonstrates CNOT gates and 3 rotation gates R_X,R_Y,R_Z. The CNOT gates force quantum entanglement between any 2 quantum circuits, allowing the qubits from the circuits can be entangled.

Then the measurement operators should be projected by measuring the expectation values of 4 observables, locally estimated for each qubit:

$$\widehat{\mathit{z}}=\left[{\widehat{\mathit{z}}}_1,{\widehat{\mathit{z}}}_2,{\widehat{\mathit{z}}}_3,{\widehat{\mathit{z}}}_{\mathit{n}}\right]$$

(8)

$$\mathsf{{\rm M}}:\mathit{z}=〈\mathit{x}\left|\widehat{\mathit{z}}\right|\mathit{x}〉$$

(9)

In the final classification stage, the cost function was used as cross entropy and via a LogSoftMax layer. The flowchart of our proposed method is shown in Figure 4, and numerical simulations were conducted using the PyTorch interface and the PennyLane software.

Table 1. The Algorithm of the hybrid classical-quantum transferring CNN.

Algorithm Hybrid classical-quantum transferring CNN

INPUT: RSI data as training data, rest RSIs dataset as test data. OUTPUT: Generate the predicted category labels. Prepare a ResNet 34 network with the autoencoder. Encode the RSI dataset . Traning: a 4-qubits tensor quantum circuit. Feed the RSI dataset to the tensor quantum circuit. Testing: Feed the rest RSI dataset to the tensor quantum circuit. STOP ALGORITHM.

Table 1. The Algorithm of the hybrid classical-quantum transferring CNN.

Algorithm Hybrid classical-quantum transferring CNN

INPUT: RSI data as training data, rest RSIs dataset as test data. OUTPUT: Generate the predicted category labels. Prepare a ResNet 34 network with the autoencoder. Encode the RSI dataset . Traning: a 4-qubits tensor quantum circuit. Feed the RSI dataset to the tensor quantum circuit. Testing: Feed the rest RSI dataset to the tensor quantum circuit. STOP ALGORITHM.

4. Evaluation an Results

In this section, we assess the hybrid classical-quantum transferring CNN in terms of performance gains for RSI scene classification.

4.1. Data Profile

Our proposed method was evaluated using two challenging RSI datasets: the EuroSat dataset and the Aerial Image dataset (AID) [19,20,38]. The EuroSat dataset contains images taken from the Sentinel-2 satellite, categorizing the ground objects into ten distinct land cover categories. The collection includes approximately 27,000 images divided across 10 classes, with patches measuring 64 × 64 pixels. The data was originally hyperspectral images captured with 13 spectral bands, but we used only RGB channels. he AID dataset includes 10,000 images of size 600×600 pixels, classified into 30 scene classes, with varying numbers of images for each label ranging from 220 to 420. The ground resolution also varies from approximately 8m to 0.5m per pixel. Figure 6 shows examples of the AID dataset.

Figure 5. This outline shows all sample images of all 10 categories covered in the EuroSAT dataset. The images size has 64 × 64 pixels. Each category contains 2000 to 3000 images. In sum, the dataset has 27,000 georefenced images [19,20].

Figure 5. This outline shows all sample images of all 10 categories covered in the EuroSAT dataset. The images size has 64 × 64 pixels. Each category contains 2000 to 3000 images. In sum, the dataset has 27,000 georefenced images [19,20].

4.2. Evaluation Criteria

There exist two extensively used evaluation criteria in RSISC: overall accuracy (OA) and confusion matrix. OA is an evaluating indicator of the classifier’s performance on the whole test data set and is defined as the sum of accurately classified samples divided by the sum of tested samples. It’s a commonly used to evaluate the performance of RSISC. The confusion matrix is an informative table used to analyse all the errors and confusions between different classes, generated by comparing the performance of correct and incorrect classification of each single classifier.

The definition of the calculation of OA can be expressed as follow:

$$\mathbf{O}\mathbf{A}=\frac{\sum _{\mathbf{i}=1}^{\mathbf{n}}{\sum }_{\mathbf{j}=1}^{\mathbf{k}}{\mathbf{P}}_{\mathbf{i}\mathbf{j}}}{\mathbf{T}}$$

(13)

where P_ij is the correct prediction of each single label, and n, k represents the sum of each label and the sum of labels. T is the sum of test dataset.

4.3. Experimental Setup

We split two different RSI datasets in different training-test ratios (10/90 ratio and 20/80 ratio) class-wise. The RGB images vast majority of all aerial and RSI datasets. For performance measurement, we compare with the performance of the proposed algorithm, the Bag-of-Viusal-Words(BoVW) approach with SIFT features, a trained SVM and other deep learning algorithms for accuracy evaluation. Furthermore, we trained a shallow CNN, a ResNet50 and a GoogleNet model on the training dataset [32,33,34,35,36]. For our proposed method, we trained a ResNet34 model and the tensor quantum circuit with the model for 60 epochs over the training dataset, with a quantum depth of 6 and an initial learning rate of η =0.0006. The model was validated with respect to the test dataset after each epoch, and overall classification on the datasets was calculated.

We used many commonly used RSISC for instance ResNet50 [15],DCNNs [73], AlexNet [44] and VGG-VD16 [47] as criteria to assess the performance improvement of our proposed method. The aforementioned models were pre-trained on ImageNet dataset and then fine-tune them to adopt them to the RSIs. For the open source AID dataset [37], the training-test ratios were set to 20%/80% and 50%/50%.

4.4. Performance Comparison

Furthermore, in order to further verify the efficiency and feasibility of the proposed algorithm in this paper, the proposed algorithm was also compared with other RSISC algorithms for experimental analysis and validated on the validation set. The results showed that the proposed algorithm achieved the best classification result (%), as shown in Table 2.

As can be seen from Table 2, we can analysis the performance of different approaches on the EuroSAT RGB dataset using various training-test splits. We evaluated four frequently used methods, including BovW, CNN, ResNet50, and GoogleNet, as baselines to assess the performance improvement of the hybrid classical-quantum transferring CNN. We used these pre-trained models on the ImageNet dataset and fine-tuned them on the EuroSAT dataset. For ResNet50 and GoogleNet, we replaced the flatten layer, maintaining the original image sizes. The proposed method exhibited better classification accuracy than other methods and significantly reduced model complexity.

To quantitatively evaluate the performance of our proposed method, we adopt the OA and confusion matrix as the evaluation metrics. OA is recorded as the number of correctly classified samples divided by the total number of samples. In the confusion matrix, each column denotes the prediction results, and each row denotes the actual ground objects of the class data. It can display the distribution of each class, and can be recommended for the analysis of miscalssification results between different classes.

Figure 7. Confusion matrix of the proposed method on the EuroSAT dataset in a training and a test set (10/90 ratio) using RSIs in the RGB color space.

Figure 7. Confusion matrix of the proposed method on the EuroSAT dataset in a training and a test set (10/90 ratio) using RSIs in the RGB color space.

As can be seen from Table 2, all CNN algorithms surpassed the BoVW method and the classification result of whole deep CNNs perform better than the classification result of shallow CNNs. Nevertheless, the proposed method achieved a classification result of up to 95.81% in a training and a test dataset (10/90 ratio) for the EuroSAT RSISC. The optimization process is demonstrated in Figure 8. As can be seen from Figure 9, the images of two scene labels are absolutely alike to each other, resulting in imperfect classification results compared with other labels.

Figure 7. Relation between the loss function and training step of the proposed method.

Figure 7. Relation between the loss function and training step of the proposed method.

Table 2 shows the resulted classification accuracies for the best performing DL models CNN models、 GoogLeNet、ResNet50 and the proposed method. In experiments with the GoogLeNet、ResNet50、CNN models and the proposed method, all models were pre-trained on the EuroSAT dataset. For a better comparison of performance of all fine-tuning models, we trained the last layer with a learning rate between 0,01 and 0,0001. Using the proposed method, we achieved a classification accuracy of about 17% better than the pre-trained model GoogleNet which have been trained on the EuroSAT dataset in the same training-test dataset ratio setting.

Figure 9. The images misclassified as others. (a,b) The images of highways misclassified as rivers. (c,d) The images of rivers misclassified as highways.

Figure 9. The images misclassified as others. (a,b) The images of highways misclassified as rivers. (c,d) The images of rivers misclassified as highways.

Furthermore, we compared the proposed algorithm with other pre-trained CNN-based classification methods for different training-test ratios on the RSI dataset. As shown in the table below, the hybrid classical-quantum transferring CNN achieved higher accuracy than other pre-trained CNN-based classification methods. The proposed algorithm can also enhance the classification result for the large scale of input images and performs better than all of the other algorithms under the training ratio of 20% and 50%, and “*” indicates the best result among all methods. The best classification results can be obtained by the algorithm that achieves 97.33% and 98.82% for the training ratios of 20% and 50%, respectively. Our proposed approach exhibits the performance of the most advanced methods.

Table 3. Contrast of the classification accuracies (%) of different training-test ratios on the AID dataset（training ratio=20% and 50%).

Method	20/80	50/50
VGG-VD16[38]	86.59	89.64
GoogLeNet [38]	83.44	86.39
AlexNet+MSCP [39]	88.99	92.36
VGG-VD16+MSCP [39]	91.52	94.42
AlexNet+SPP [40]	87.44	91.45
RADCNet [41]	88.12	92.53
AlexNet+SAFF [42]	87.51	91.83
VGG-VD16+SAFF [42]	90.25	93.83
AlexNet+RIR [43]	91.95	94.56
VGG-VD16+RIR [43]	93.34	95.57
ResNet50+RIR [43]	94.95	96.48
DCNN [44]	90.82	96.89
CBAM [45]	94.66	96.90
MSCP [46]	92.21	96.56
Two-Stream Fusion [47]	92.32	94.58
RTN [48]	92.44	_
GCFs+LOFs [49]	92.48	96.85
CapsNet [50]	91.63	94.74
ARCNet [51]	88.75	93.1
SCCov [52]	93.12	96.1
KFBNet [53]	95.50	97.40
GBNet [54]	92.20	95.48
MG-CAP [55]	93.34	96.12
EAM [56]	94.26	97.06
EAM [56]	93.64	96.62
F2BRBM [57]	96.05	96.97
MBLANet [58]	95.60	97.14
GRMANet [59]	95.43	97.39
IDCCP [60]	94.80	96.95
MSANet [61]	93.53	96.01
CTNet [62]	96.25	97.70
LSENet [63]	94.41	96.36
DFAGCN [64]	_	94.88
MGML-FENet [65]	96.45	98.60
ESD-MBENet-v1[66]	96.20	98.85*
ESD-MBENet-v2[66]	96.39	98.40
SeCo-ResNet-50[67]	93.47	95.99
RSP-ViTAEv2-S [68]	96.91*	98.22
ISP(ViT) [69]	96.24	97.95
ISSP(ViT) [70]	95.82	97.98
RingMo(ViT-200W-200E) [71]	96.54	98.38
ISP(Swin) [72]	96.24	98.03
ISSP(Swin) [73]	96.54	97.95
RingMo(Swin-200W-200E) [71]	96.90	98.34
Ours	97.33	98.82

Table 3. Contrast of the classification accuracies (%) of different training-test ratios on the AID dataset（training ratio=20% and 50%).

Method	20/80	50/50
VGG-VD16[38]	86.59	89.64
GoogLeNet [38]	83.44	86.39
AlexNet+MSCP [39]	88.99	92.36
VGG-VD16+MSCP [39]	91.52	94.42
AlexNet+SPP [40]	87.44	91.45
RADCNet [41]	88.12	92.53
AlexNet+SAFF [42]	87.51	91.83
VGG-VD16+SAFF [42]	90.25	93.83
AlexNet+RIR [43]	91.95	94.56
VGG-VD16+RIR [43]	93.34	95.57
ResNet50+RIR [43]	94.95	96.48
DCNN [44]	90.82	96.89
CBAM [45]	94.66	96.90
MSCP [46]	92.21	96.56
Two-Stream Fusion [47]	92.32	94.58
RTN [48]	92.44	_
GCFs+LOFs [49]	92.48	96.85
CapsNet [50]	91.63	94.74
ARCNet [51]	88.75	93.1
SCCov [52]	93.12	96.1
KFBNet [53]	95.50	97.40
GBNet [54]	92.20	95.48
MG-CAP [55]	93.34	96.12
EAM [56]	94.26	97.06
EAM [56]	93.64	96.62
F2BRBM [57]	96.05	96.97
MBLANet [58]	95.60	97.14
GRMANet [59]	95.43	97.39
IDCCP [60]	94.80	96.95
MSANet [61]	93.53	96.01
CTNet [62]	96.25	97.70
LSENet [63]	94.41	96.36
DFAGCN [64]	_	94.88
MGML-FENet [65]	96.45	98.60
ESD-MBENet-v1[66]	96.20	98.85*
ESD-MBENet-v2[66]	96.39	98.40
SeCo-ResNet-50[67]	93.47	95.99
RSP-ViTAEv2-S [68]	96.91*	98.22
ISP(ViT) [69]	96.24	97.95
ISSP(ViT) [70]	95.82	97.98
RingMo(ViT-200W-200E) [71]	96.54	98.38
ISP(Swin) [72]	96.24	98.03
ISSP(Swin) [73]	96.54	97.95
RingMo(Swin-200W-200E) [71]	96.90	98.34
Ours	97.33	98.82

We have implemented these networks using a neural network library named Pytorch and a cross-platform Python library for quantum computing named PennyLane [74,75]. The experiments have been operated on a computer graphics workstation equipped with a single AMD Ryzen Threadripper PRO 3945WX 12-Cores CPU and a single NVIDIA GeForce NVIDIA RTX A5000 24GB GPU.

5. Conclusions

Over the past decade, rapid development has provided us with massive remote sensing datasets for intelligent earth observation using RSIs. However, the lack of publicly available “big data” of RSIs severely limits the development of new approaches especially quantum machine learning methods. This work first presents the background of classical networks, variation quantum circuits and tensor quantum circuits. Then, a hybrid classical-quantum transferring CNN applied to RSISC is proposed. The main advantage of the proposed method is that it allows the input images to be of various shapes and sizes dispense with resizing of such images prior to the processing. It preserves key feature information in high spatial resolution images, which is greatly beneficial to ultimately achieve better classification performance. In comparison to other deep learning methods with the same number of training samples, the proposed method has achieved amazing scene classification results. Data annotation must be done manually by skilled professionals of the area of RSISC. When RSI dataset is massive, data annotation can become more complicated because of the huge diversities and variations in RSIs. Most of these models require a large-scale labeled dataset and numerous iterations to train their parameter sets. The experimental results show that the proposed method can achieve satisfied classification results with fewer number of training samples. This means that in the application of RSISC, the increased workload of data annotation can be reduced manually by skilled professionals. In order to improve classification accuracy, the sum of the CNNs layer has expanded from few layers to hundred layers. Usually the vast majority of models have huge parameters, moreover operation of the CNN models require a enormous labeled datasets for models training and powerful equipment wtih high-performance GPUs for notable performance improvements of operation, which severely limits the development of RSISC methods. However, in compare with huge CNNs, the proposed method is a compact、lightweight and efficient RSISC model with fewer parameters. On the other side, the proposed method is extremely expensive and time-consuming due to the limitations of cross-platform for differentiable programming of quantum computers. In the future, the method should be improved in quantum circuit simulators with support for automatic differentiation, just-in-time compiling, hardware acceleration, and vectorized parallelism. Especially when the quantum circuit size or the batch dimension is large, the new platform can bring speedup in quantum circuit simulation.