ABSTRACT A quantum K‐nearest neighbors(QKNN) algorithm is proposed to offer superior performance compared to the classical KNN(CKNN) approach, improving classification accuracy, scalability, and robustness. Our approach optimizes Hadamard and rotation gates for quantum data encoding and efficiently embeds classical data into quantum states. Entangled gates, such as IsingXY and CNOT, enhance feature extraction and classification by enabling complex feature interactions. A new quantum distance metric based on swap test results is used to calculate similarity measures between quantum states. This algorithm offers superior accuracy and computational efficiency compared to traditional Euclidean distance metrics. We used three benchmark datasets to evaluate the suggested QKNN method. The results demonstrated that it outperformed the other two methods, classical KNN (CKNN) and quantum neural networks (QNN), as well as the more recent QKNN research. The proposed QKNN algorithm achieves prediction accuracies of 98.25%, 100%, and 99.27% for the three datasets, whereas the QNN achieves prediction accuracies of 97.17%, 83.33%, and 86.18%, respectively. Moreover, quantum noise challenges are addressed by integrating a Shor code‐based error mitigation strategy, which ensures stability of the algorithm and resilience to noisy quantum environments. The results demonstrate the scalability, efficiency, and robustness of the proposed QKNN algorithm.
ABSTRACT A quantum K‐nearest neighbors(QKNN) algorithm is proposed to offer superior performance compared to the classical KNN(CKNN) approach, improving classification accuracy, scalability, and robustness. Our approach optimizes Hadamard and rotation gates for quantum data encoding and efficiently embeds classical data into quantum states. Entangled gates, such as IsingXY and CNOT, enhance feature extraction and classification by enabling complex feature interactions. A new quantum distance metric based on swap test results is used to calculate similarity measures between quantum states. This algorithm offers superior accuracy and computational efficiency compared to traditional Euclidean distance metrics. We used three benchmark datasets to evaluate the suggested QKNN method. The results demonstrated that it outperformed the other two methods, classical KNN (CKNN) and quantum neural networks (QNN), as well as the more recent QKNN research. The proposed QKNN algorithm achieves prediction accuracies of 98.25%, 100%, and 99.27% for the three datasets, whereas the QNN achieves prediction accuracies of 97.17%, 83.33%, and 86.18%, respectively. Moreover, quantum noise challenges are addressed by integrating a Shor code‐based error mitigation strategy, which ensures stability of the algorithm and resilience to noisy quantum environments. The results demonstrate the scalability, efficiency, and robustness of the proposed QKNN algorithm.
This paper presents a novel quantum K-nearest neighbors (QKNN) algorithm, which offers improved performance over the classical k-NN technique by incorporating quantum computing (QC) techniques to enhance classification accuracy, scalability, and robustness. The proposed modifications focus on optimizing quantum data encoding using Hadamard and rotation gates, ensuring more effective rendering of classical data in quantum states. In addition, the quantum feature extraction process is significantly enhanced by the use of entangled gates such as IsingXY and CNOT, which enables better feature interactions and class separability. A novel quantum distance metric, based on the swap test, is introduced to calculate similarity measures between various quantum states, offering superior accuracy and computational efficiency compared to traditional Euclidean distance metrics. We assess the achievement of the proposed QKNN algorithm on three benchmark datasets: Wisconsin Breast Cancer, Iris, and Bank Note Authentication, and have noted its superior performance relative to both classical k-NN (CKNN) and Quantum Neural Network (QNN). The proposed QKNN algorithm is found to achieve prediction accuracies of 98.25%, 100%, and 99.27% ,respectively, for the three datasets, while the customized QNN shows prediction accuracies of only 97.17%, 83.33%, and 86.18%, respectively. Furthermore, we address the challenges of quantum noise by incorporating a repetition encoding-based error mitigation strategy, which ensures the stability and resilience of the algorithm in noisy quantum environments. The results highlight the potential of the proposed QKNN as a scalable, efficient and robust quantum-enhanced machine learning algorithm, especially in high-dimensional and complex datasets, when traditional approaches frequently fail.
Abstract Text classification, a key process in natural language processing (NLP), relies on the k‐nearest neighbors (KNN) algorithm for its simplicity and effectiveness. Traditional methods often grapple with the high‐dimensional nature of textual data, leading to substantial computational demands. This study introduces a novel classical quantum k‐nearest neighbors (CQKNN) algorithm, which integrates quantum circuits into a conventional machine‐learning framework to enhance computational efficiency and reduce storage requirements. This hybrid approach uses a unified quantum circuit that simplifies multiple similarity calculations through mid‐circuit measurements and qubit reset operations, significantly improving upon traditional multi‐circuit quantum k‐nearest neighbors (QKNN) models. The CQKNN algorithm, tested on datasets such as SMS Spam Collection, Twitter US Airline Sentiment, and IMDB Movie Reviews, not only outperforms classical KNN but also addresses challenges posed by noisy intermediate‐scale quantum (NISQ) devices through advanced error mitigation techniques. This work highlights resource efficiency and reduced gate complexity and demonstrates the practical application of fidelity in quantum similarity calculations, setting new standards for quantum‐enhanced machine learning and advancing current quantum technology capabilities in complex data classification tasks.
Dealing with high-dimensional data is a well-known limitation for the classic K-Nearest Neighbors (KNN) algorithm, creating substantial computational and memory overhead. While Quantum Machine Learning (QML) presents a compelling alternative, many existing Quantum KNN (QKNN) frameworks are largely theoretical, remaining impractical for current hardware due to their significant qubit demands. This paper introduces the Fidelity-Based Quantum K-Nearest Neighbors (FQKNN) algorithm, a method specifically designed for feasibility on near-term devices. Our primary contribution is the use of quantum fidelity as a similarity function, which offers a more nuanced metric than conventional distance calculations. This is combined with an efficient amplitude encoding strategy that logarithmically scales the qubit requirement to just log2(N) for an N-dimensional feature vector. This combination makes FQKNN a resource-efficient and practical algorithm. We validated its performance on the benchmark Iris and Breast Cancer datasets, achieving classification accuracies of 96.7% and 93.3% respectively, surpassing the performance of the classical KNN baseline. These findings not only confirm the viability of our fidelity-based similarity measure but also underscore the demonstrable potential of QML to enhance classification tasks.
One of the simplest and most effective classical machine learning algorithms is the k-nearest neighbors algorithm (kNN) which classifies an unknown test state by finding the k nearest neighbors from a set of M train states. Here we present a quantum analog of classical kNN − quantum kNN (QkNN) − based on fidelity as the similarity measure. We show that QkNN algorithm can be reduced to an instance of the quantum k-maxima algorithm, hence the query complexity of QkNN is O(kM). The non-trivial task in this reduction is to encode the fidelity information between the test state and all the train states as amplitudes of a quantum state. Converting this amplitude encoded information to a digital format enables us to compare them efficiently, thus completing the reduction. Unlike classical kNN and existing quantum kNN algorithms, the proposed algorithm can be directly used on quantum data thereby bypassing expensive processes such as quantum state tomography. As an example, we show the applicability of this algorithm in entanglement classification and quantum state discrimination.
The K-nearest neighbor (KNN) algorithm is one of the most extensively used classification algorithms, while its high time complexity limits its performance in the era of big data. The quantum K-nearest neighbor (QKNN) algorithm can handle the above problem with satisfactory efficiency; however, its accuracy is sacrificed when directly applying the traditional similarity measure based on Euclidean distance. Inspired by the Polar coordinate system and the quantum property, this work proposes a new similarity measure to replace the Euclidean distance, which is defined as Polar distance. Polar distance considers both angular and module length information, introducing a weight parameter adjusted to the specific application data. To validate the efficiency of Polar distance, we conducted various experiments using several typical datasets. For the conventional KNN algorithm, the accuracy performance is comparable when using Polar distance for similarity measurement, while for the QKNN algorithm, it significantly outperforms the Euclidean distance in terms of classification accuracy. Furthermore, the Polar distance shows scalability and robustness superior to the Euclidean distance, providing an opportunity for the large-scale application of QKNN in practice.
Quantum computing has risen as the new type of computer that theoretically reduces the time complexity of classical methods exponentially because of the nature of superposition. It is promising to reduce runtimes on large data sets in machine learning (ML). Meanwhile, k-nearest neighbor (kNN) is a simple ML algorithm that can be translated to a quantum version (QkNN) to perform classification tasks efficiently. Here, we show a new version of QkNN which has a speed up in time complexity by using a new design of quantum circuits called integrated swap test. This quantum circuit can load two N-dimensional states and calculate the fidelity between them. Results show that QkNN allows us to take a different approach to the ML field.