Multiclass seismic damage detection of buildings using quantum convolutional neural network

The traditional visual inspection technique for damage assessment of buildings immediately after an earthquake can be time‐consuming, labor‐intensive, and risky. Numerous studies have been carried out using deep learning techniques, particularly convolutional neural network (CNN), to evaluate the damage to building structures after an earthquake using buildings’ damage images. Quantum computing, on the other hand, is a computing environment that can exploit superposition and entanglement, which are not available in classical computing environments, to achieve higher performance using parallelism between qubits. This paper presents a novel quantum CNN (QCNN) approach to detect damage to reinforced concrete (RC) buildings from images after the earthquake. The QCNN model is developed and trained using the RC building damaged images collected from past earthquakes. The performance of this model is evaluated based on the multiclass damage detection ability of the real‐world RC building damaged images collected from the recent earthquake in Turkey in February 2023. Furthermore, the seismic damage detection accuracy obtained from the QCNN model is compared with various CNN architecture results.

post-earthquake rescue, relief, and recovery operations.People become homeless when an earthquake occurs for two reasons: (1) damage to the building structures and (2) there is no timely or accurate evaluation of the seismic damage to building structures.To enable residents to return to their homes and workplaces in a safe and timely way, a methodology is needed to carry out a fast assessment of damage induced to buildings due to an earthquake.The majority of current seismic reconnaissance techniques are manual.A group of experts or certified inspectors visits the earthquake-affected areas, collecting the damage information of the building structures, post-processing the damage details, and finally proposing the decision such as safe, unsafe, retrofit, collapse, and so forth.This technique is a time-consuming and labor-intensive method.For example, it took about 3 weeks and a couple of months for the damage evaluation of buildings after the 2017 Mexico earthquake (Hoskere et al., 2018a) and the 2015 Nepal earthquake (Sajan et al., 2023), respectively.Furthermore, there may be insufficient experts to be mobilized to the earthquake-affected area at the same time, and the safety of the inspectors cannot be guaranteed in the aftermath of the earthquake.
With the rapid enhancement in computational capability in recent times, the use of artificial intelligence (AI) has increased significantly for rapid inspection and damage assessment of structures (Bhatta & Dang, 2023;Rafiei & Adeli, 2017b).Deep learning (DL)-based convolutional neural network (CNN) has gained significant attention across all disciplines due to its improved detection accuracy and speed.The viability of using CNN for effective and autonomous prediction of different structural damages has been explored in the past (Han et al., 2022;Gopalakrishnan et al., 2017;Dogan et al., 2023).Lingxin et al. (2022) presented a comprehensive literature review on current developments in damage detection using DLbased techniques in recent years.Pan and Yang (2022) presented a real-time DL model for monitoring bolt loosening and rotation assessment.Gao and Mosalam (2018) used the DL technique to detect the component types of damage, such as beam, column, or wall, and check the spalling and no spalling condition.Ghosh Mondal et al. (2020) used region-based CNN (Faster RCNN) to detect different buildings' damage, such as surface cracks, spalling, spalling with exposed rebars, and severely buckled rebars.Cha et al. (2017) used CNN to detect concrete cracks using different lightening conditions.Liang (2019) proposed DL-based post-disaster assessment of reinforced concrete (RC) bridges in three levels such as system level, component level, and local damage detection.Yeum et al. (2018) demonstrated the CNN technique and its capabilities to classify collapse or non-collapse buildings and to detect spalling in concrete structures using images collected from past earthquake events.Narazaki et al. (2018) used multiscale CNN to identify bridge components.Zhang et al. (2017) presented a deep-learning technique to identify the pavement crack on 3D asphalt surfaces.Hoskere et al. (2018b) used deep CNN to recognize six different types of damage in civil infrastructure systems.Cha et al. (2018) explored RCNN to detect multiple damage categories (DCs), such as concrete cracks, steel corrosion, bolt corrosion, and steel delamination.Pan and Yang (2020) used dual CNN to detect damage after the earthquake and estimated the repair cost of RC buildings.Shrestha and Dang (2020) Kim et al. (2018) investigated the use of RCNN to detect cracks in a concrete bridge that were monitored using an unmanned aerial vehicle (UAV).Lin et al. (2017) proposed a DL-based structural damage detection method to extract features from low-level sensor data automatically.
In the past decade, notable advancements have been made in DL-related systems (Naranjo et al., 2021;Xue et al., 2021) andapplications (Alzubaidi et al., 2021).Due to the limit of semiconductor fabrication technology along with the exponential growth in the data size, the advancement of learning algorithms has slowed down in the post-Moore's Law period (Stein et al., 2022).An estimated 2.5 exabytes of data are produced every day (T.M. Khan & Robles-Kelly, 2020), and the era of computers in the classical meaning has reached its apogee and is coming to an end (Kuros & Kryjak, 2023).The growth of these data exceeds that of computing capacity.The rapid advancement of Graphics Processing Unit (GPU) for parallel processing has addressed some of the problems with big data in classical computation by giving a significant boost to deep neural networks (T.M. Khan & Robles-Kelly, 2020).However, there are still some issues that are too challenging to resolve, and some of these can be solved using quantum computing.Quantum computing, on the other hand, is a computing environment that is different from conventional computers and is provided through the use of quantum computers.Superposition and entanglement, which are not present in classical computing environments, can be used by quantum computers, in particular, to achieve high performance through parallelism amongst qubits (Bravyi et al., 2018).This enables the use of quantum machine learning (QML) when datasets grow exponentially and are difficult to solve by the classical machine learning (ML) models.In recent years, the field of QML has grown quickly as evidenced by the recent surge in QML papers (S.Y. C. Chen et al., 2022;Rebentrost et al., 2014;Singh & Muchahari, 2023).The current status of the QML field is summarized in a number of research articles (Biamonte et al., 2017;Dunjko & Briegel, 2018;García et al., 2022).The development of quantum CNN (QCNN) algorithms has been motivated by the benefits of CNN, together with the potential power of QML (Hur et al., 2022;Kerenidis et al., 2019;Y. Li et al., 2020) in various fields.The adoption of QNN has increased in medical sectors to classify medical images as evidenced by this research work (Alsharabi et al., 2023;Z. Li et al., 2022;Houssein et al., 2022).The potential advantage of using hybrid QNN for drug response prediction is demonstrated by Sagingalieva et al. (2022), where the availability of training data is limited.Peng and Li (2007) achieved excellent results in implementing QNN to detect facial expressions in the Japanese female facial expression database.F. Li et al. (2002) and Yang et al. (2021) explored QNN for speech recognition.Furthermore, Hernández et al. (2020) used a quantum classifier to classify images of digits on two different databases: the digits dataset and the Semeion dataset.Zhou et al., Suen (1999) adopted a quantum neural network (QNN) with fuzzy features to detect handwritten numerals.Several research works (Potempa & Porebski, 2022;Riaz et al., 2023;Trochun et al., 2021) proposed QCNN algorithms to classify images of MNIST datasets (Yann et al., 1999) and MNIST Fashion datasets (Henderson et al., 2020;Xiao et al., 2017).Likewise, the adoption of QCNNs techniques in classifying images of the CIFAR-10 dataset (Krizhevsky & Hinton, 2009) has been reported in the literature (Riaz et al., 2023;Raj & Vaithiyashankar, 2022).They revealed that the QCNN model outperformed the classical CNN in terms of accuracy and convergence speed and showed the potentiality of using QCNN for multiclass classification problems.Wei et al. (2022) developed a QCNN model for handwritten number recognition and modeled three kinds of image filtering, including edge detection, sharpening, and smoothing.Yu and Ma (2008) investigated the capability of using QNN for vehicle classification.Kuros and Kryjak (2023) used hybrid quantum-classical CNN to classify traffic signs.Although its performance did not outperform classical CNN, it showed the potential of using QCNN for classification problems.Arthur (2022) investigated the feasibility of a hybrid quantum-classical neural network architecture implementing variational quantum circuits on a series of binary classification datasets.Likewise, Z. Khan et al. (2021) developed a hybrid quantum-classical neural network to detect traffic incidents using connected vehicle data and evaluated its performance against classical ML models.Majumder et al. (2021) obtained better classification accuracy using a hybrid classical-quantum DL model for the autonomous classification of vehicle traffic images under adversarial attack than classical-only ML models.Aytekin et al. (2014) exploited an automatic object segmentation method using quantum cuts.Trochun et al. (2021) presented a QCNN for binary image classification to detect damaged buildings on satellite images.The better performance of the QCNN model over pretrained models such as VGG-15 and RESNET-50 suggested the feasibility of adopting QCNN for multiclass classi-fication problems.Mogalapalli et al. (2022) proposed a quantum transfer learning-based method for three distinct image classification tasks: categorizing organic and recyclable waste, recognizing tuberculosis from chest X-ray images, and identifying the presence of cracks from concrete crack images.For the processing of point cloud data in classification applications, a 3D scalable QCNN model is proposed by Baek et al. (2022).These research works are carried out to check the feasibility of using QCNN in terms of larger datasets, higher accuracy, and computational time as compared with CNN and suggested that QCNN is better than CNN in this regard.However, this study is now focused on examining the performance of QCNN over classical DL techniques.The study on larger datasets and computational speed is considered a future work as this study incorporates smaller datasets and no quantum computer is used.No research work has been reported to date using the QCNN approach to detect the RC building damage images into multiple categories.Thus, this research aims to check the feasibility of using QCNN to detect the RC building's damage after an earthquake and compare its result with other CNN architecture's damage detection results.For this, the damaged images of RC buildings are collected from past earthquakes across the world.The images are classified into five different categories such as no or slight damage, moderate damage, heavy damage, very heavy damage, and collapse, following the European Macroseismic Scale (EMS) guidelines (Grünthal, 1998).The QCNN model is trained using past earthquake-induced damage images of RC buildings.The performance of this trained model is evaluated based on its performance on unseen damaged images, which are collected after the recent Turkey earthquake in February 2023 (W.Chen et al., 2023).Moreover, the comparison is made between the QCNN model performance with the results of various deep CNN architectures, such as AlexNet, Visual Geometric Group with 16 convolutional layers (VGG-16) and 19 convolutional layers (VGG-19), Residual Network with 50 deep layers (ResNet50), InceptionV2, InceptionV3, MobileNetV2, Xception, and DenseNet.Figure 1 illustrates the overall methodology adopted in this study.

Quantum bits or qubits
In classical computing, a bit is the fundamental unit of information that, at a given instance of time, can exist in either a 0 or 1 state.Quantum bits, also known as qubits, are the basic memory units in quantum computing that can exist in a superposition of both the states 0 and 1.In the realm of quantum mechanics, the computational basis states corresponding to 0 and 1 can be represented using Dirac notation as shown in Equation ( 1), and thus Equation (2) expressed the state of a single-qubit as a linear combination of the basis states |0⟩ and |1⟩.A quantum computer that consists of n qubits can exist in 2 n superposition states, that is, from |000. . .0⟩ to |111. . .1⟩.This quantum characteristic allows for exponential speedups in many computation works that would take classical algorithms eons to complete.
where  and  are the complex number, and Equation ( 2) tells us about the qubit in a state that has the probability of || positive x-axis with the projection of |Ψ⟩ measuring in an anticlockwise direction and varies in the range of 0 ≤  ≤ 2π.Any points on the block sphere correspond to a qubit state.The states of a qubit in the x, y, and z axes of the block sphere are shown in Table 1.
TA B L E 1 Qubit states on x, y, and z axes.

Axis
Value of  and  Qubit state

Quantum gates
Data are encoded by quantum states, while quantum gates are used to perform operations on quantum states.Quantum gates perform a change on a quantum state to create a new quantum state.

Single-qubit gates
To manipulate the state of the bits in classical computing, various gates, such as OR, AND, NOT, XOR, and so forth, are used.In quantum computing, quantum gates are employed to manipulate the states of the qubits.

Quantum NOT Gate
A classical NOT gate converts the bit's state, for example, from the existing state 0 to 1, and vice-versa.Similar operations are carried out by a quantum gate but in terms of the amplitudes of the computational basis states of qubits.The probability amplitude of the |0⟩ state is assigned to the |1⟩ state, and vice versa.The quantum NOT gate functions as an operator X, as demonstrated in Equation ( 4), and can be written as Equation ( 5) in the matrix form.
The overall probability ought to remain constant under the transformation of a quantum gate.The probability is conserved in the case of the NOT gate as is evident.In principle, any quantum gate needs to abide by just one property; they must be unitary matrices, to guarantee that the probability is conserved.

Hadamard gate
The Hadamard gate transforms a qubit's state into an equal superposition state.It transforms the |0⟩ state and |1⟩ state to their respective superposition state as shown in Equations ( 6) and ( 7), respectively.As explained in Figure 2, the Hadamard gate transforms the state |0⟩ aligned along the z-axis into the state |1⟩ aligned along the positive x-axis.The unitary matrix representing the Hadamard gate (H) is shown in Equation ( 8).Furthermore, the identity matrix is obtained by calculating the square of the Hadamard matrix, which signifies that the state of the qubit does not alter if the Hadamard gate is applied twice consecutively.

Quantum Z gate
The quantum Z gate leaves state |0⟩ intact while changing state |1⟩ to −|1⟩.The representation of the transformation of the quantum Z gate is shown in Equation ( 9), which can also be described as the outer products of the computational basis states.This implies that the Z gate transforms any given arbitrary state |Ψ⟩ = | 0⟩ + | 1⟩ to the state | 0⟩-| 1⟩.

Multiple-qubit gates
the matrix representation of CNOT gate.

Controlled-U gate
The controlled-U gate, as shown in Figure 3, is a multiqubit gate that works for n number of qubits.Consider a quantum system with n qubits and a unitary operator U. Assume a controlled-U gate as one that employs the unitary operator U on the system of n target qubits based on the state of a control qubit.The system of n target qubits receives no transformation when the control qubit is in state |0⟩; however, unitary operator is employed on the system of n target qubits when the control qubit is in state |1⟩.
In fact, the CNOT gate is a special case of the controlled-U gate, with the single-qubit X gate serving as the unitary operator.

Quantum entanglement
Quantum computing utilizes the properties of quantum states, such as superposition and entanglement, to execute computation.Superposition is a phenomenon in which the qubit can exist in both the state of 0 and 1.Along with superposition, quantum entanglement is another phenomenon in which the exchange of quantum information between two particles occurs even though they are separated by a large distance.This typically implies that the results of a measurement on one qubit reveal information about the other.

ARCHITECTURE
CNN is a well-known DL algorithm and model that has had a significant impact in the area of AI and ML.
It is extensively used in image recognition and object detection for classification purposes.CNN primarily focuses on the basis that the inputs will comprised images.
The general architecture of CNN comprised three types of layers, convolutional layers, pooling layers, and fully connected layers.CNN architecture is formed by stacking these layers.In CNN, an input array is applied with alternating convolutional layers (with an activation function), followed by the pooling layers and some fully connected layers before the output.A simple CNN architecture for the classification of building damage images acquired in this study is illustrated in Figure 4a, which consists of two convolutional layers with 64 kernels of size 3 × 3 and rectified linear unit (ReLU) activation function, two max pooling layers of size 2 × 2 after each convolutional layer, a flattened layer, and a dense layer with SoftMax function before the output.As the name implies, the convolutional layer is critical to how CNN operates.Each CNN layer consists of N convolutional filters or also known as kernels.
Although these kernels typically have low spatial dimensions, they cover the full depth of the input.Each filter in a convolutional layer is convolved throughout the spatial dimensions of the input to create a 2D feature map.The scalar product is computed for each value in that kernel as it moves through the input as shown in Figure 4b.
The result of the convolutional layer is a tensor of N feature maps, each of which contains details about various spatially local patterns in the data.The pooling layers aim to gradually reduce the size of the feature map, reducing the number of parameters and model computational complexity and avoiding overfitting.The classification result is achieved using the fully connected layer once the data size has been adequately reduced by repeatedly applying the convolutional layer and pooling layer.The model is compiled with the adaptive moment estimation (Adam) optimizer and the loss function as the sparse categorical cross-entropy with the accuracy metric.

ARCHITECTURE
The implementation of the QCNN model aims to enhance the CNN performance to detect the multiclass DCs of RC buildings' damaged images.Here, the QCNN model is a hybrid computation-based model where the quantum convolutional layer is applied initially proposed by Henderson et al. (2020) and is followed by a classical CNN structure as shown in Figure 5. QCNN is simply an expansion of conventional CNN that includes an extra transformational layer known as the quantum convolutional layer as shown in Figure 5b.In this case, the quantum convolutional layer that integrates into the CNN architecture is identical to that of traditional convolutional layers.The key difference is that in CNN, the convolutional filters (also known as the kernel) present in the convolutional layers extract features from the input images performing dot products of the matrix between the subregion of the input image and kernel as shown in Figure 4b, whereas in QCNN, quantum convolutional filters utilize the random quantum circuit, which takes input spatially local subsections of images from the dataset as explained in Figure 5b.The qubits are initialized with the pixel data corresponding to the filter size in the encoding process, and the decoding process yields new classical data after measurement.This process is repeated to complete the new feature map.Similar to the classical convolutional layer, the quantum convolutional layer consists of quantum filters applied to the input image.The primary idea behind quantum convolution is to use the random quantum circuit to split input images into small local areas in order to extract relevant features.The advantage of the quantum circuit in quantum convolution is that it works with a few quantum bits and shallow depth of quantum circuits.Generally, the overall process adopted in this approach is explained in Figure 6.It includes mainly three steps, (1) preprocessing of damaged images, (2) application of quantum circuit as a convolutional filter, and (3) classical CNN structure.
The approach proposed in this study is implemented on a quantum computing simulator using Python (version 3.7.0)and PennyLane libraries (release 0.27.0;Bergholm et al., 2018).The built-in RandomLayers and Strong-lyEntanglingLayers functions of PennyLane were used to create the random quantum circuit and highly entangled quantum circuit.The quantum PennyLane device is initialized to resemble a system of the four-qubit device.The random quantum circuit operates on 2 × 2 small squares of an input image.The input data are converted into the rotation angles of quantum states using the angle encoding method.The rotational gate around the y-axis (RY gate) encodes each 2 × 2 square of the image into a quantum state.The encoding process is repeated, considering various patches of the 2 × 2 square of the input image.This is equivalent to a convolution with a 2 × 2 kernel and a stride of 2 in the classical convolution process.The random quantum circuit of four qubits is chosen to be compatible with 2 × 2 squares of an input image.A random quantum circuit is made up of a succession of quantum unitary operations (gates) and measurements connected by wires (qubits).The number of random layers is set to one since this parameter did not influence the detecting results, which is also verified in (Koros & Kryjak, 2023).The four expectation values are mapped into four different channels of a single output pixel.Figure 7 shows the four output channels produced by the quantum convolution in grayscale.The figure further illustrates the downsampling of the resolution and some local distortion that occurred by the quantum convolutional filter.The global shape of the image, on the other hand, remains preserved as expected for a convolution layer.The features obtained after using the quantum convolution layer are then fed into a conventional neural network, which is trained to categorize the damaged images.Similar to the CNN architecture discussed in Section 3, QCNN consists of a quantum convolutional layer, two convolutional layers followed by the rectified linear unit activation function, and two max-pooling layers followed by the two fully connected layers.The model is compiled using a similar optimizer, loss function, and metrics used in the CNN model.The method is implemented in DESKTOP-CORKGE3, having 8GB RAM and Intel(R) Core (TM) i7-10700 @ 2.90 GHz processor.

DEVELOP A MODEL AND EVALUATE ITS PERFORMANCE
This study presents the multiclass damage detection of RC buildings' damaged images after an earthquake using a QCNN.The past earthquake damage images collected from various sources such as datacenterhub.org(Shah et al., 2015;Sim et al., 2016), earthquake damage-related published research articles, earthquake damage reports, and Google search for damage images after an earthquake are used in this study for the evaluation of the proposed approach.Diversity in training damage images is essential for reducing model variance, which measures how sensitive the model is to specific observations.A learning model with high diversity works well on training images.However, the performance decreases when the model is tested on unseen images.The problem of model variance can be solved by considering damage images observed after the earthquake events experienced in different parts of the world in the training database.In other words, the higher diversity of damaged images in the database results in a more reliable damage detection capability of the training model.The model trained using the damage images collected from many earthquake events is supposed to be more robust when tested on unseen damage images.To create a robust universal model considering various forms of damage, the damage images of RC buildings are collected from different earthquakes events that occurred in the past, such as the 2001 Gujarat earthquake (7.6 Mw), 2005 Pakistan earthquake (7.6 Mw), 2008 Sichuan F I G U R E 7 Sample of input images preprocessed by the random quantum circuit.earthquake (7.9 Mw), 2009 L'Aquila earthquake (6.3 Mw), 2010 Chile earthquake (8.8 Mw), 2015 Nepal earthquake (7.8 Mw), 2016 Kumamoto earthquake (7.0 Mw), 2016 Ecuador earthquake (7.8 Mw), 2020 Zagreb earthquake (5.4 Mw), and 2022 Sichuan earthquake (6.8 Mw), where the overall damaged images for each class constitute around 50% from the 2015 Nepal earthquake, 10% from 2022 Sichuan earthquake, and around 5% from other earthquakes events as shown in Figure 8.All the damaged images that are collected from past earthquake events are classified into five DCs, (1) DC0: no to slight damage, (2) DC1: moderate damage, (3) DC2: heavy damage, (4) DC3: very heavy damage, and (5) DC4: collapse, following the EMS-98 (Grünthal, 1998) guidelines as illustrated in Table 2, and the sample damaged images are shown in Figure 9.A total of 2043 training images and 260 testing images are considered in this study.Figure 10 shows the number of training and testing images used in this study for each DC.
Unlike research works (Dogan et al., 2023;Ghosh Mondal et al., 2020;Yeum et al., 2018), in this study, CNN and QCNN models are trained using damage images collected from many past earthquake events, and their performance is evaluated based on the multiclass damage detecting capability when encountered with unseen RC building damage images collected from the recent earthquake in Turkey.The sample images for each class as shown in Figure 11.The testing database contains 52 damage images for each DC as shown in Figure 10.Furthermore, the performance of these models is evaluated based on evaluation metrics such as accuracy, precision, recall, and f1-score.
A higher accuracy of nearly 100% indicates the higher efficacy of these models in detecting the multiclass DCs of RC building damage images.Precision refers to the percentage of predicted DCs that are correctly assigned by these models, whereas recall refers to the percentage of actual DCs that are correctly assigned by these models.The harmonic mean of decision and recall is known as the  Figure 12 shows the performance of the QCNN and CNN model on training images in the form of a confusion matrix.The overall DCs detection accuracy is found to be higher in the case of QCNN than CNN.
Furthermore, higher precision and recall value of each DC is observed in the case of QCNN, whereas these values are found to be comparatively lower in the case of CNN.Likewise, Figure 13 shows the confusion matrix of these models on testing images.The QCNN and CNN models achieved an overall DCs detection accuracy of 61.2% and 56.9%, respectively, on testing images.The higher recall value of 100% for DC4 is obtained using QCNN than CNN, with 78.8%.The performance of these models in detecting DC0 is found to be similar.However, the recall values obtained from these models for DC1, DC2, and DC3 are found to be comparatively lower, that is, less than 41%, except for DC3 in the case of CNN, with 51.9%.Besides, the test accuracy and loss learning curves obtained from the QCNN and CNN models are depicted in Figure 14.Overall, in this study, the QCNN model is found to be comparatively better than CNN in detecting the multiclass DC of damage images collected after the 2023 Turkey earthquake.This shows the capability of using QCNN to detect multiclass damage of RC buildings after an earthquake.The proposed approach can be computationally efficient adopting the quantum computer.However, the computational time taken to train the QCNN model is observed as 55 min, which is comparatively higher than CNN model, which can be built in less than 5 min for this dataset.Running the analysis in quantum computers such as IBM-Q to investigate the performance of QCNN on larger datasets and examine the computational efficiency is considered as future work.

COMPARISON WITH VARIOUS CNN ARCHITECTURES
The previous section discussed the performance of the models developed in Sections 4 and 5 on the unseen damage images where the CNN architecture has a simple architecture of two layers.However, most of the frontrunners in image processing and computer vision contests currently employ deep CNN-based models.Deep CNNs outperform shallow systems in representing specific function classes and are computationally more efficient for complicated operations (Delalleau & Bengio, 2011).In this section, the performance of the QCNN model is compared with various widely adopted CNN architectures.During the process, fine-tuning is done while using the various deep CNN architectures.The top layers of the pre-trained models are frozen and used the pre-trained ImageNet weights.Furthermore, the output layer is modified with a SoftMax layer of five categories.In addition, the Adam optimizer is used, and sparse categorical cross-entropy loss is considered to compile the model.Figures 15 and 16 show the damage detection results of various deep CNN architectures such as AlexNet, VGG-16, VGG-19, ResNet50, InceptionV2 InceptionV3, MobileNetV2, Xception, and DenseNet on testing images.The comparison curve of the overall damage-detecting accuracy of various models is summarized in Figure 17.The detecting capability of DC0 and DC4 is found to be higher for all the models.However, higher confusion is observed in detecting DC1 and DC2.Surprisingly ResNet50 could not have a single correct detection for class DC1.Likewise, only 5, 6, and 7 correct detections for the class DC1 are obtained from AlexNet, VGG16, and MobileNetV2 models, respectively.For DC2, Alexnet, DenseNet, and MobileNetV2 could have only 7, 7, and 3 correct DC detections.Overall, DenseNet and MobileNetV2 have obtained higher and lower detection accuracy of 58.8% and 44.9%, respectively, on the unseen damage images collected after the recent Turkey earthquake.Furthermore, the box and whisker plot shown in Figure 18 compares the performance of QCNN and various deep CNN models in detecting the multiclass DC in terms of the f1-score.The lower and higher point represents the smallest and the largest f1-score values considering f1-score values from DC1-DC4.Similarly, the lower and higher box point and the horizontal line and "x" mark inside the box represents the second quartile (the value below which the lower 25% of the data are contained), third quartile (the value above which the upper 25% of the data are contained), median (middle value), and mean (average of all DC, DC1-DC4) respectively.The plot shows that the smallest f1-score value and the higher average value are obtained using the QCNN model.Hence, in this study, the QCNN model outperforms these deep CNN architectures models considered in this study.This proves the feasibility of using QCNN in detecting the multiclass DC of buildings using damaged images.It shows that QCNN enhances CNN performance by incorporating quantum environments.

CONCLUSION AND FUTURE WORKS
In this study, a novel QCNN approach is presented to detect multiclass damage to RC buildings from images after the earthquake.The QCNN model is trained using RC building's damaged images collected after many earthquakes experienced in the past.The performance of the developed model is evaluated in detecting the multiclass damage on unseen damage images collected after the recent earthquake event in Turkey in 2023.Furthermore, considering larger datasets to train the model.In this study, the simplest encoding method, that is, angle encoding, is used to transform input data into rotation angles of quantum states.Considering other encoding techniques (such as amplitude encoding) and additional quantum convolutional layers in the structure to identify the alteration in detection accuracy will be the main focus of future work.
With the help of QCNN, different strategies are made possible by a CNN model and a quantum computing environment.In addition to the existing CNN model, the QCNN model may be a solution to solve the problems as a more effective and efficient learning model and for highlevel outcomes in more difficult and extensive learning in the NISQ-era quantum computer (Preskill, 2018).It is now conceivable to think about what is next for quantum DL and QCNN in particular.The proposed approach can be beneficial for damage recognition and damage type iden-tification in various civil engineering infrastructures.In addition to image identification, quantum techniques are now being explored for fields including natural language processing, such as the work of Galofaro et al. (2018) to identify hate speech.Additionally, quantum hardware has advanced, with organizations like PsiQuantum attempting to create million-qubit quantum processors.Despite the difficulties in using QNNs that have been demonstrated, we can still anticipate additional developments in quantum DL as long as the research is conducted at the "juncture" of DL and quantum computing.The implementation of the QCNN model is difficult; however, the research works may find a way to integrate this QCNN model with hardware such as iPhone or UAV to detect damage in real time in the near future.Furthermore, there is a huge possibility to continue further research on hybrid quantum algorithms or the adoption of newly developed developed a DL model to classify the ambient, device bias, earthquake, and traffic vibration data and implemented it in real time using a smartphone.Al-Deen Taher and Dang (2022) examined the feasibility of multiple damage detection and segmentation using Mask R-CNN.R. Li et al. (2018) used a unified vision-based technique to detect near-real-time concrete defects and classify them under challenging conditions with geolocalization.Zhao et al. (2018) adopted AlexNet-based CNN for bridge classification, Zeiler and Fergus network (ZF-net)-based faster R-CNN for bridge component recognition, and GoogleNetbased CNN to detect cracks in bridges.
2 and || 2 appearing in | 0⟩ and | 1⟩ state, respectively.A block sphere is a geometrical representation of all possible states of a qubit as illustrated in Figure 2. Equation (3) gives the simplified block sphere representation of a qubit state (Pattanayak, 2021) in terms of two parameters,  and , where  is the angle made by z-the axis with |Ψ⟩ and varies in the range of 0 ≤  ≤ π, and  is the angle made byF I G U R E 2 Block sphere representation of a qubit.

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Block diagram of convolutional neural network (CNN) architecture.F I G U R E 5 Block diagram of quantum CNN (QCNN) architecture.

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I G U R E 6 Flowchart of the QCNN model.DC, damage category.

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I G U R E 8 (a) Proportion of damage images collected from past earthquakes and (b) source of damaged images.F I G U R E 9 Sample of damaged images used for training.(a) No/slight damage, (b) moderate damage, (c) heavy damage, (d) very heavy damage, and (e) collapse.F I G U R E 1 0 Number of training and testing images on each damage category.DC, damage category; RC, reinforced concrete.

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Damaged images collected after the Turkey earthquake 2023.(a) No/slight damage, (b) moderate damage, (c) heavy damage, (d) very heavy damage, and (e) collapse.F I G U R E 1 2 Confusion matrix on training images (a) QCNN and (b) CNN.DC, damage category.TA B L E 2 Classification of damaged images into five categories.near collapse of the building f1-score.A good classifier is expected to have a precision, recall, and f1-score of approximately 1 (high).

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Confusion matrix on testing images (a) QCNN and (b) CNN.DC, damage category.F I G U R E 1 4 Comparison between QCNN and CNN (a) accuracy curve and (b) loss curve.

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Confusion matrix of various CNN architectures on testing images.DC, damage category.

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Confusion matrix of various deep learning architectures on testing images (a) InceptionV2, (b) InceptionV3, (c) MobileNetV2, (d) Xception, and (e) DenseNet.DC, damage category.the performance of the QCNN model is compared with the damage detection results of various DL model architectures.The overall damage detection accuracy obtained from the QCNN model is found to be higher than other deep CNN model architectures.This shows the capability of using QCNN in detecting the multiclass damage of RC buildings from images after the earthquake.However, the damage detection accuracy can be increased by F I G U R E 1 7 Overall accuracy obtained from various CNN architectures on testing images.F I G U R E 1 8 f1-score of QCNN and various CNN architectures on testing images.
controlled NOT gate, also known as a CNOT gate, is one of the two-qubit gates that is used in creating universal quantum gates.In this case, two qubits, qubit A and qubit B are generally referred to as the control bit and target bit, respectively.The control qubit state does not change upon the application of a CNOT gate.However, the target qubit state is reversed if the control qubit exists in the state | 1⟩.The quantum state |Ψ⟩ =  00 |00⟩+  01 |01⟩+  10 |10⟩+ A 11 |11⟩ is changed into the state new |Ψ new⟩ =  00 |00⟩+  01 |01⟩+  11 |10⟩+  10 |11⟩where the first qubit is the control qubit, and the second qubit is the target qubit to the CNOT gate as illustrated in Equation (10), where U CN is