Quantum K-means clustering method for detecting heart disease using quantum circuit approach.

The development of noisy intermediate- scale quantum computers is expected to signify the potential advantages of quantum computing over classical computing. This paper focuses on quantum paradigm usage to speed up unsupervised machine learning algorithms particularly the K-means clustering method. The main approach is to build a quantum circuit that performs the distance calculation required for the clustering process. This proposed technique is a collaboration of data mining techniques with quantum computation. Initially, extracted heart disease dataset is preprocessed and classical K-means clustering performance is evaluated. Later, the quantum concept is applied to the classical approach of the clustering algorithm. The comparative analysis is performed between quantum and classical processing to check performance metrics.

Introduction

Machine learning (ML) plays a vital role in solving various highly challenging tasks due to its ability to handle computational improvements. Although computing power has grown rapidly in recent decades and new algorithms have hit the market regularly, the growth in data has outpaced the growth in computing power. As a result, in the field of artificial intelligence, which in many cases relies on massive data, a lack of computational capacity eventually becomes a shortcoming. As the dataset becomes huge, it requires fast and efficient algorithms to process. Polynomial-time algorithms are not always thought to be the most efficient as it takes more time to process it Xu and Tian (2015). One of the fields, where it is becoming difficult to handle the increasing data management, is the healthcare sector.

Despite significant medical improvements, heart failure continues to pose a significant hazard to patients’ health. Currently, doctors must manually diagnose and anticipate the condition based on their knowledge, experience, and observations. It poses a challenge for healthcare practitioners since it results in extremely high rates of mortality and morbidity (Abdel-Basset et al. 2020). Developing healthcare systems based on patient data models and technologies can significantly improve the decision-making process. Despite the fact that the medical industry collects a large amount of data, it must be processed accurately and rapidly to provide an early and automated diagnosis. Furthermore, various machine learning (ML) algorithms have demonstrated promising results in the diagnosis of heart disorders, and they were used to solve a variety of complex issues with efficient and accurate outcomes (Rani et al. 2021; Katarya and Meena 2021; Bakhsh 2021). The ability of ML algorithms to learn the relationship between input data and output class using standard probability and logic theories is one of the fundamental issues. However, even with faster ML methods, there exists a computational bottleneck on handling large data for traditional computers. Hence to enhance the computational power, a new paradigm quantum computers came into existence.

Quantum mechanics (QM) has also been shown to outperform classical theory-based models in a variety of disciplines (including classification, object detection, object tracking, prediction, and optimization) (Shao et al. 2019; Biamonte et al. 2017). With a burgeoning amount of data, existing machine learning algorithms are finding it difficult to tackle computationally intensive tasks. In this aspect, quantum computing power may provide a competitive advantage in machine learning applications (Möller and Vuik 2017). As a result, quantum computing and medical systems provide hardware sophisticated results that allow the healthcare industry to evaluate and treat complicated medical disorders. Thus, it is concluded that both classical and quantum machine learning methods contribute to the earlier detection of heart diseases and the identification of predictive traits in various pathological states (Kumar et al. 2021). Based on these, the heart disease dataset chosen has to be properly preprocessed before applying machine learning algorithms (Yang and Nataliani 2017; Wettschereck et al. 1997). The various state of the art carried out to understand and find a new approach to diagnose heart disease at early stage is discussed in next section

Related work and motivation

Various researchers had made different approach to implement clustering QML algorithm. Bharill et al. (2015) use an improved quantum-inspired evolutionary fuzzy C-means (EQIE-FCM) algorithm to calculate the global optima of the parameters. The author uses “quantum K-means” and “quantum fuzzy C-means” clustering approach to predict diabetes. The limitation was imposed on calculating the processing time required to form the clustering. Aïmeur et al. (2013) propose divisive clustering, k-medians clustering methods to form clustering on random data. Grover search approach is used for distance calculation and form cluster. The author only proposes the theoretical concepts on how the black-box model is used to query the distance between pairs of points. Lacks to construct the quantum circuit that has the same functionality as the black box to perform clustering. Casaña-Eslava et al. (2020) focus of the work is on developing a new algorithm for cluster allocation with autonomous hyper-parameter selection, and efficient computation has not been analyzed deeply. For cluster identification by density, the authors adopt the Schrödinger equation to deal with local length parameters. The probabilistic quantum clustering (PQC) was implemented on real and synthetic datasets.

Yao et al. (2008) propose the main benefit and drawback of the quantum clustering algorithm (QC). The authors explored the improved algorithm—exponent distance-based quantum clustering algorithm (EQDC) based on its shortcomings observed in QC. This (EQDC) approach was implemented on the IRIS dataset. No preprocessing was applied to data before analyzing EQDC. The processing time required to form the clustering and other performance factors is not mentioned. Singh and Bose (2021) in this paper, “fast forward quantum optimization algorithm (FFQOA)” along with “K-means clustering (KMC) algorithm” was used to segment chest CT images of COVID-19 patients. The FFQOAK technique was only tested with chest images. The future work was imposed to work with distinct medical images, such as X-rays and MRIs, as well as a variety of engineering design challenges. Li et al. (2011) integrate the concept of quantum walks (QWs) with the problem of data clustering and develop two clustering algorithms based on one-dimensional discrete-time QWs. The proposed QML algorithms are implemented on Soybean, Iris, Sonar, Glass, Ionosphere, and Breast cancer Wisconsin datasets. Simulated only on classical machines. No quantum processing operations are performed.

Arthur (2021) present a quantum approach to solve the balanced K-means clustering training by exploring quadratic unconstrained binary optimization (QUBO). The balanced K-means clustering method was imposed on the IRIS dataset. The dataset chosen is not so computationally expensive as quantum can process large datasets at a faster speed. Farouk (2017) uses a labeled dataset of Arabic vowels to be applied on the QC algorithm. The accuracy and processing time of non-hierarchical kernel techniques for unsupervised clusterings, such as K-means, self-organizing map (SOM), and fuzzy C-means (FCM), are then computed. The K-means, SOM, and FCM methods are applied to process speech data. Implemented in MATLAB with no intervention of quantum processor. The usage of all available data on Arabic vowels is limited due to processing time constraints. Kumar et al. (2021) propose a comparison of classical and quantum-enhanced machine learning techniques to predict patients’ diabetes. The quantum-enhanced machine learning was implemented on the PIDD dataset. Improper rotation of quantum logic gates in quantum computers is prone to induce inaccuracies, which resulted in erroneous output. Khan et al. (2019) build K-means clustering based on (i) quantum interference, (ii) negative rotations, and (iii) destructive interference. The proposed K-means clustering method was implemented using the IRIS dataset, MNIST dataset. Lacks to address qubit’s coherence times and noise which reduces the effect on solving problems with high accuracy.

Inspired by the work carried out by various researchers in the field of quantum unsupervised learning, the proposed work highlights the use of the quantum K-means approach to predict heart disease with significant improvements in clustering performance compared to classical machines.

The main motivation of this work is—the existing ML models are generally characterized by a sophisticated quantum of data that leads to process overhead (Haq et al. 2018; Mohan et al. 2019). Most of the healthcare datasets available are observed to be very huge as it has to store all the information in order to have a proper prediction. This high dimensionality of the data makes it difficult to visualize even in 3D, referred to as the curse of dimensionality (Keogh and Mueen 2017). As a result, performing operations on this data requires a lot of memory, and the data can grow exponentially at times, leading to overfitting. The weighting features are utilized to eliminate redundancy in the heart disease dataset, which helps to speed up the execution time and thereby predict the disease precisely at early stages. Here the quantum computer comes into the picture which has a high speed of computing due to its parallelism feature and can solve specific algorithms with distinct problems (Kerenidis et al. 2018; Sarma et al. 2019). To execute machine learning algorithms on a quantum computer, the classical algorithms must be redesigned to adhere to quantum mechanics principles (Ramezani et al. 2020). Quantum primitive-based algorithms for supervised (Acampora 2019) and reinforcement learning (Lamata 2021) have already been developed. However, with the exception of a quantum technique for the minimal spanning tree, limited work has been done on unsupervised learning related to the healthcare domain. Several quantum clustering algorithms use Grover’s search and show a speedup over their classical counterparts, but they are unable to increase the quality of the clustering process (Rubio et al. 2017). From this motivations, the contribution of the proposed work is summarized in the next subsection

Contribution

In this work, we contribute three major aspects of quantum K-means method an unsupervised learning with the focus on quantum circuit approach.Unsupervised quantum algorithm implementation on NISQ computers based on quantum circuits can provide better results considering the number of gates required to build the circuit. Executing these ML algorithms on a quantum system reduces processing overhead and also improves/matches with performance metrics of classical systems. Therefore, this work focuses on how well the quantum computing paradigm can be utilized to perform clustering and speed up the processing time of unsupervised learning and also other performance measures such as accuracy, precision, F1-score, sensitivity, and specificity.

First, we propose different quantum data preparation method to convert classical data into quantum state. From this, the best data preparation method based on performance metrics is chosen for further processing.

Second, we provide quantum circuit approach to calculate distance between centroid and datapoints. We repeat the iteration of centroid and cluster updation until the convergence is reached.

Third, we show the effectiveness of quantum clustering with classical clustering with experimental results, which exhibits the efficacy of the proposed method.

Finally, the performance evaluation of the proposed work is compared with other state-of-the-art methods. The improvement in the proposed method results is due to the less time taken by quantum processor to form the clusters with proposed data preparation and distance calculation methods.

The rest of this article is organized in the following order. The methodology incorporated to predict heart disease using classical and quantum approach is discussed in Sect. 2. In Sect. 3, we explain the classical K-means algorithm to cluster the heart disease dataset. Next, we explain the quantum K-means approach for clustering the heart disease dataset in Sect. 4. We present experimental results and comparisons of quantum K-means using quantum circuits with classical in Sect. 5 and finally, Sect. 6 presents the conclusion with future work.

Methodology

Methodology carried out to predict heart disease in classical and quantum context using K-means clustering method is shown in Fig. 1

Fig. 1

Process flow for clustering

Classical data preparation, preprocessing and K-means approach: Heart disease dataset chosen is preprocessed to check NULL values, and use relevant normalization techniques such as standard scalar and PCA scalar to scale all features and identify and eliminate outliers to obtain better performance metrics. Finally classical K-means algorithm is implemented to evaluate accuracy, precision, sensitivity, specificity, and F1-score.

Quantum data preparation: All the classical data are converted to quantum state by applying different data preparation methods. The best data preparation method is chosen for further processing.

Distance calculation using quantum swap test circuit and cluster and centroid updation: After data preprocessing (normalization and outlier rejection) quantum K-means algorithm is implemented to evaluate all performance measures as that of classical to relate the comparative analysis.

Finally the quantum cluster formed should be relatively or equally comparable with the classical cluster formed, along with this performance metrics and processing time between two machines are recorded.

Also state-of-the-art comparison is carried out to exhibit the performance of the proposed method.

Heart disease prediction data description

The data content of the heart disease prediction consists of a collection of records, representing the diagnosis of the patient heart disease (Al-Yarimi et al. 2021). The extracted dataset was the Public Health dataset (Gangal 2021). It contains 13 features including the predicting attribute. Since the chosen dataset contains 8 categorical data, it is handled by converting to integer during preprocessing stage as shown in Table 1. data The “target” field indicates whether or not the patient has cardiac disease. Target = “0” refers to no disease and Target = “1” refers presence of disease. A total of 1025 patients record are summarized for the prediction of cardiac disease. The first two columns tabulate the “age” and “sex” of the patient. The rest of the columns describe the type of chest pain, resting blood pressure value, cholesterol level, fasting blood sugar value, resting electrocardiographic results, maximum heart rate, exercise-induced angina, Oldpeak referring to ST depression, the slope of ST segment (Bharti et al. 2021). Hence it is difficult for the classical machines to process the huge data, and it has to be preprocessed before applying K-means algorithm. Next section explains various preprocessing steps such as feature selection and reduction techniques, outlier removal techniques, and data visualization.

Table 1

Preprocessing dataset by converting category to integer

Attributes	Type	Data encoding (Category to integer)
sex	Category	Male:1, Female:2
chest_pain_type	Category	Typical angina:1, Non-anginal pain:2, Atypical angina:3,’Asymptomatic:4
fasting_blood_sugar	Category	Lower_than_120:1, Greater_than_120:2
rest_ecg	Category	ST_T wave abnormality:1, Normal:2, Left ventricular hypertrophy:3
Exercise_induced_angina	Category	No:1, Yes:2
slope	Category	Flat:0, Downsloping:1, Upsloping:2
vessels_colored_by_flourosopy	Category	Zero:1, One:2, Two:3, Three:4, Four:5
thalassemia	Category	Fixed Defect:0, Reversable Defect:1, Normal:2, No:3

Dimensionality reduction technique and feature selection

Increasing dimensionality results in computationally expensive and poor performance of clustering algorithms. The principal component analysis (PCA) and standard MinMax scaler are used to compress higher-dimensional data for dimensionality reduction of the dataset. Setting the dimensionality to 2 has the added benefit that clusters can be visualized appropriately. Standard scaling and MinMax scaling are used to scale the data to a fixed range from +1 to -1. As a result, the standard deviations are minimized.

Outlier removal technique

As the dataset is not properly distributed and consists of many outliers, data have to undergo preprocessing. Initially, the amount of outliers present in the dataset is detected. These outliers are removed from data using the mathematical function Inter Quartile Range(IQR). Using the quartile method find Q1 and Q3 values, which are then subtracted (Q3–Q1) to obtain IQR. Lower bound(Q1 - 1.5 * IQR) and upper bound (Q3 + 1.5 * IQR) values are used to check outlier and this outlier can be easily removed from data as shown in Fig. 2.

Fig. 2

Outlier visualization

Data visualization

During preprocessing, the pairs plot visualization technique is used to see the distribution of single variables and the relationship between two variables. This helps to find the most separated clusters. Based on the dataset analysis oldpeak, vessels_colored_by_flourosopy, resting_blood_pressure, rest_ecg features are dropped. Figure 3 shows the correlation among features and hence chosen for subsequent analysis. After the data preprocessing, classical K-means approach to form the cluster is applied. Next section details the algorithm used to implement classical K-means clustering.

Fig. 3

Pair plot of 13 features

Classical K-means clustering method

K-means clustering (Na et al. 2010) is an unsupervised clustering method first proposed by Lloyd (1982). It is one of the most used clustering techniques. Let represent the datapoints, where each row element consists of “M” number of features. Clustering of datapoints is driven by a set of centroids : generated from the dataset X. Thus set of datapoints is divided into K-clusters by reducing “weighted sum of squared errors” (WSSE) given by “Elbow method” Shi et al. (2021). As shown in Fig. 4, the k value is selected as 2.The classical K-means algorithm (Huang 1998) described below iterates between two major steps: 1) updating of the clusters and 2) updating of the centroids.

Fig. 4

Elbow plot for selecting k value in cluster

The time complexity of the algorithm is specified by O(LNpK), where L = number of iterations taken to form clusters, N = number of datapoints, p = dataset dimension, K = centroids. Since the time taken to process such a huge data is more in classical machines, we now analyze the working of clustering processing using quantum systems. Next section briefs the quantum K-means clustering approach in detail.

Quantum K-means clustering

The initial step to achieve the quantum machine learning process is to convert the data points into quantum states (Benlamine et al. 2020). Following that, the distance between each state’s centroids is computed. In terms of quantum learning, estimating the distance between quantum states is completely different from classical learning. The distance computation in the classical version is performed using coordinates, whereas in quantum learning the distance calculation is exhibited in terms of the probabilistic nature of qubits. Although quantum learning allows for the measurement and quantification of notions such as phase differences and amplitudes of different probabilities, the calculation of the distance between two states is unfortunately not achievable due to quantum noise and instability (Gong et al. 2021).

Set to be the centroid cluster in the chosen dataset and to be the new datapoint used to find for which cluster it belongs to. To find the distance between these two vectors, one more ancillary qubit in state is used. A Hadamard gate is appended to qubit to bring it to a superposed state. Using swap gate controlled on the auxiliary qubit, the distance from the state to the entangled state of the ancillary qubit is computed. The ancillary qubit is then subjected to another Hadamard gate before being measured. After determining the distance between the states and and the centroid, a swap test circuit is used to assign each state to its nearest cluster. Iterative steps are carried out by updating new centroids of each cluster till the stop criterion is satisfied. Quantum K-means clustering is concluded in three subroutines: 1) distance calculation using swap test circuit, 2) cluster updation, and 3) centroid updation.

After preprocessing steps (similar to classical method), data preparation and distance calculation is followed to convert classical data to quantum state and process. In quantum systems, due to the limited memory, the original data cannot be used directly to process clustering. Therefore the data is normalized and then data preparation methods are applied. Next sections explains the different data preparation methods and distance calculation method to update cluster and centroid

Data preparation and distance calculation using swap test circuit

Prior to computing the distance between two vectors, it is necessary to encode the data from classical to quantum state. By using the rotation gate each data point is assigned to a specific point on the Bloch-sphere. On chosen heart disease dataset, many state-preparation approaches are applied and tested. Various types of state preparation methods are- This analogue encoding task of mapping data into the large Hilbert space is referred as “Angle encoding” given byIn a quantum context, datapoint assignment to the relative cluster is achieved by the overlap function, which measures the state of overlap between two vectors (Zhang and Ni 2020). Outputting “1” indicates, two vectors are identical, and “0” indicates they are orthogonal or no overlap found. Turning this analogy to quantum part requires a swap test that results in a squared probability of the overlap shown in Fig. 5.

Fig. 5

Quantum-swap-test-circuit

U3 rotation gate (one rotation angle) : Where rotation angle is determined by the values of data point features (Shende et al. 2006). Then rotations are applied to to match the datapoints.

U3 rotation gate (two rotation angles) : Rotation angles and are used to map the data points. (Liu et al. 2010). Then rotations are applied to to encode these angles into qubits.

Ry and Rz rotations : To transform all the qubit-state to the , initial rotation is applied to Z-axis and then to Y-axis.

Initially, two quantum states and and one ancillary qubit are chosen, and its outer product is given asApplying Hadamard gate to the ancillary qubit, a superposition state is obtained as:The controlled “SWAP gate” is then applied to the states and in order to swap the states and with the target qubit . This results inAnother “Hadamard gate” is placed in the ancillary qubit at the end, resulting in:Expanding the above equation results in:Finally, the measurement is applied to the ancillary qubit (Benlamine et al. 2020). The probability of getting state is given by,If the probability value = 0.5, the two states and are orthogonal or have no overlap, and if , the two states are identical. Similarly, is specified byFurthermore, distance between 2 states is computed bywhere d = input nonzero data points, = maximum limit of any feature in the data. Thus the overlap function leads a foundation to perform clustering tasks. To form the final cluster, after every distance calculation cluster and centroid updation are performed iteratively. this cluster and centroid updation is similar to classical method summarized in next subsections.

Cluster updation

The nearest-neighbor function is used to allocate the new data point to the closest cluster after computing the distance from the new data point to each cluster centroid (Sergioli et al. 2018). Cluster assignment is given by

Centroid updation

Centroids are recomputed by taking the mean of all the datapoints assigned to a particular cluster. Centroid updation is given byThese three phases are performed until the cluster centroid’s position does not change, indicating convergence. The algorithm for Q K-means is summarized below:

Result and analysis

The performance measures between the two approaches were evaluated in terms of accuracy, precision, sensitivity, specificity, and F1-score. The evaluating parameters are given below:

Accuracy is the measure of the system’s ability to make correct predictions. It is given byThe system ability to make correct positive predictions is given by sensitivity and correct negative predictions are given by specificityPrecision evaluates the system capability to produce only relevant results.F1-score gives the harmonic mean of precision and sensitivity. A higher F1-score represents better modeling.Initially Classical K-means approach for predicting heart disease was implemented on the original dataset and results are tabulated. The normalization steps such as standard scaling, min-max scaling, and PCA are applied clean and high-quality data with reduced features, which promises good performance metrics. Finally, to have better clustering outliers rejection (OR) is performed and clustering is evaluated to check the performance. The results obtained are shown in Table 2.

Table 2

Classical K-means performance for heart disease dataset

Heart disease dataset	Accuracy	Precision	Sensitivity	Specificity	F1-score
Original	85	87	85	86	86
After normalization	93	93	95	94	94
After outlier rejection	94	95	94	94	93

Similarly, to check the performance of clustering of the proposed method, the methodology flow shown in Sect. 2 is followed. The number of gates that can be executed and the number of qubits that can be used in a given algorithm are both limited in IBM Q experience. This dataset is preprocessed before distance calculation for clustering. By using principal component analysis(PCA), the heart disease dataset consisting of 1025 features are reduced to 2 features. Quantum computers could also be used for dimensionality reduction algorithms such as (Cong and Duan 2016; Lloyd et al. 2014). Implementation and execution of the algorithm are carried out in IBM’s open-source quantum software development kit QISKIT Aleksandrowicz et al. (2019). Qiskit allows access to several quantum simulators both locally and in the cloud. A state vector simulator can simulate circuits with up to 25 qubits, whereas a unitary simulator can simulate circuits with up to 12 qubits.

On choosing different data preparation methods in the QML approach, evaluation parameters are measured. This data preparation is applied before all the preprocessing steps to check the better performance with different rotations. The results obtained are tabulated in Table 3.

Table 3

Performance measure for different data preparation methods

Data preparation method	Accuracy	Precision	Sensitivity	Specificity	F1-score
Rz,Ry	90	91	88	90	91
U3(θ,0,0)	93	92	91	93	92
U3(θ,φ,π)	95	95	94	92	94

From running the quantum K-means method using different rotation methods, the best obtained performance measure is selected for further processing. Due to the limitations imposed on quantum computers, initially, data have to be preprocessed by normalization and then Q-K means is applied. Same as classical, quantum K-means method is applied to data after normalization and after outlier rejection, and results obtained in quantum laboratories from Qiskit are tabulated in Table 4.

Table 4

Quantum K-means performance for heart disease dataset

Heart disease dataset	Accuracy	Precision	Sensitivity	Specificity	F1-score
After normalization	95	95	94	92	94
After outlier rejection	96.4	96.8	95	95	96.4

Finally, the classical and quantum K-means approach is compared to present the performance evaluation shown in Fig. 6

Fig. 6

Comparison between classical and quantum K-means performance

The processing time in quantum is faster compared to classical machines. Indeed, traditional machine learning approaches take polynomial time to process and classify huge set of vector numbers in high-dimensional domains. In contrast, quantum computers may alter high-dimensional vectors in the tensor product spaces in logarithmic time (Khan et al. 2019). Table 5 shows the comparison of two algorithms based on processing time.

Table 5

Preprocessing time between classical and quantum

Heart disease dataset	Processing time (sec)
	Classical K-means	Quantum K-means
Original	1.49	–
After normalization	1.40	0.68
After outlier rejection	1.38	0.45

Hence, after combining all of the above results, along with processing time, it was observed that quantum K-means outperforms classical counterparts in measurements of accuracy, precision, sensitivity, specificity, F1-score, and processing time in predicting heart disease. Table 6 compares the results of the proposed work to other state-of-the-art approaches. The proposed approach outperforms all compared state-of-the-art methods in the detection of heart disease.

Table 6

Comparative analysis of proposed work with state-of-the-art methods

State-of-the-art	Methodology	Accuracy	Precision	Sensitivity	F1-score
Kuruvilla and Balaji (2021)	Correlation based feature selection (CBFS)	84.9	80.5	84.9	79.1
Kannan and Vasanthi (2019)	Logistic regression (LR)	86.8	81.2	84.3	82.4
Gao et al. (2021)	Bagging ensemble learning with DT and PCA	83	88	81	85
Kumar et al. (2021)	Quantum KNN (QKNN)	88	87	90	89
Gupta et al. (2021)	QML- VQC	86.3	74.4	85.2	79.2
Proposed work	Classical K-means	94	95	94	94
Proposed work	Quantum K-means	96.4	96.8	94.3	96.4

For the chosen heart disease prediction, the original data scatter and processed cluster steps are shown in Fig. 7; similarly, the clustering process carried out in the quantum system is shown in Fig. 8.

Fig. 7

Classical K-means clustering, a original scattered dataset, b clustering process iteration 1, c clustering process iteration 2, d final clustered data

Fig. 8

Quantum K-means clustering, a Original scattered dataset, b Clustering process iteration 1, c Clustering process iteration 2, d Final clustered data

Clustering achieved between classical and quantum shows relatively comparable results. Quantum k-means executed in the Qasm simulator exhibits less execution time compared to the classical system. This proves the supremacy of quantum computers in terms of speed. As the dataset becomes huge, quantum systems perform better than classical in terms of speed. The quantum circuit used to perform clustering is shown in Fig. 9.

Fig. 9

Quantum circuits for clustering

Some of the limitations imposed while processing the data from classical to quantum are-These limitations of the quantum computers provide inadvertent results for quantum algorithms with a larger number of quantum operations. To resolve this limitations, one has to design the quantum circuits with shallow depth. Therefore, the proposed quantum K-means approach to detect heart disease is implemented with simpler quantum circuits resulting in better results even on NISQ computers.

Number of available qubits and gate operations are limited. Therefore the original data is preprocessed and then fed into the system.

Lack of noise immunity in quantum operations. This small imperfections in the input data or gate operations leads to erroneous output.

Rotational gates used are more likely prone to error. Any wrong rotations can cause error in the output.

Quantum decoherence caused by heat and light results in loss of qubit’s quantum entanglement property thereby losing the stored data.

Conclusion

The possibility of quantum computers to give exponential speedups has prompted substantial research into quantum algorithms. Quantum computers currently have some constraints in terms of quantum noise and qubit coherence times. These impediments limit their ability to solve problems with reasonable precision. In this article, heart disease prediction is presented using the classical and quantum K-means method. Quantum K-means clustering is performed utilizing a set of quantum gates consisting of less number quantum operations thereby resulting in significant improvement in terms of accuracy and execution time. In contrast to traditional K-means clustering, which takes O(LNpK) time, quantum mechanical K-means clustering takes only O(LNK) time. This might save a lot of time in data mining applications, where data dimensions are typically in the hundreds.

In the future, the developed Q K-means approach can be extended to explore other healthcare datasets. Based on the analysis quantum machine learning offers a wide range of applications in the medical industry. Despite the fact that quantum machine learning increases computing performance and can handle data stored in a variety of ways, it still has limits. Qubits lose their quantum entanglement property due to quantum decoherence produced by heat and light, resulting in data loss. Also, rotations of various quantum gates are prone to generate inaccuracy and produce erroneous output. Likewise, quantum algorithms are constrained by certain simulations, which limit their use. With the fast-moving progress in technology, it is optimistic that this technique will find a lot of advancement beyond its classical counterparts.