This work introduces a quantum K-Nearest Neighbor (K-NN) classifier algorithm. The algorithm utilizes angle encoding through a Quantum Random Access Memory (QRAM) using n number of qubit addresses with O(log(n)) space complexity. It incorporates Grover’s algorithm and the quantum SWAP-Test to identify similar states and determine the nearest neighbors with high probability, achieving Om search complexity, where m is the qubit address. We implement a simulation of the algorithm using IBM’s Qiskit with GPU support, applying it to the Iris and MNIST datasets with two different angle encodings. The experiments employ multiple QRAM cell sizes (8, 16, 32, 64, 128) and perform ten trials per size. According to the performance, accuracy values in the Iris dataset range from 89.3 ± 5.78% to 94.0 ± 1.56%. The MNIST dataset’s mean binary accuracy values range from 79.45 ± 18.84% to 94.00 ± 2.11% for classes 0 and 1. Additionally, a comparison of the results of this proposed approach with different state-of-the-art versions of QK-NN and the classical K-NN using Scikit-learn. This method achieves a 96.4 ± 2.22% accuracy in the Iris dataset. Finally, this proposal contributes an experimental result to the state of the art for the MNIST dataset, achieving an accuracy of 96.55 ± 2.00%. This work presents a new implementation proposal for QK-NN and conducts multiple experiments that yield more robust results than previous implementations. Although our average performance approaches still need to surpass the classic results, an experimental increase in the size of QRAM or the amount of data to encode is not achieved due to limitations. However, our results show promising improvement when considering working with more feature numbers and accommodating more data in the QRAM.
This work introduces a quantum K-Nearest Neighbor (K-NN) classifier algorithm. The algorithm utilizes angle encoding through a Quantum Random Access Memory (QRAM) using n number of qubit addresses with O(log(n)) space complexity. It incorporates Grover’s algorithm and the quantum SWAP-Test to identify similar states and determine the nearest neighbors with high probability, achieving Om search complexity, where m is the qubit address. We implement a simulation of the algorithm using IBM’s Qiskit with GPU support, applying it to the Iris and MNIST datasets with two different angle encodings. The experiments employ multiple QRAM cell sizes (8, 16, 32, 64, 128) and perform ten trials per size. According to the performance, accuracy values in the Iris dataset range from 89.3 ± 5.78% to 94.0 ± 1.56%. The MNIST dataset’s mean binary accuracy values range from 79.45 ± 18.84% to 94.00 ± 2.11% for classes 0 and 1. Additionally, a comparison of the results of this proposed approach with different state-of-the-art versions of QK-NN and the classical K-NN using Scikit-learn. This method achieves a 96.4 ± 2.22% accuracy in the Iris dataset. Finally, this proposal contributes an experimental result to the state of the art for the MNIST dataset, achieving an accuracy of 96.55 ± 2.00%. This work presents a new implementation proposal for QK-NN and conducts multiple experiments that yield more robust results than previous implementations. Although our average performance approaches still need to surpass the classic results, an experimental increase in the size of QRAM or the amount of data to encode is not achieved due to limitations. However, our results show promising improvement when considering working with more feature numbers and accommodating more data in the QRAM.
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.
The k-nearest neighbor algorithm (k-NN) is a straightforward and highly effective classical machine learning method that categorises unidentified test instances by identifying the k-nearest Neighbors from the collection of m-training instances. It is widely acknowledged that integrating machine learning algorithms with quantum computing offers tremendous benefits in some applications involving higher dimensional datasets. This research examines the quantum k-nearest neighbor (QK-NN) algorithm executed within the PennyLane’s default. qubit framework. The paper assesses the benefits of incorporating quantum computing into machine learning problems by focusing on quantum circuits and quantum feature maps for quantum-enhanced classifiers. The PennyLane framework is employed to model the behaviour on four datasets viz. Iris, Wine, Rain, Indian Lever. The implementation results reveal that quantum-enhanced k-NN Combined feature maps exhibit superior performance on most of the Accuracy, Precision, Recall and F-1 score parameters compared to individual feature maps.
Every day, humans generate approximately 2.5 billion gigabytes of new data. While this data is crucial in applications such as drug development and cybersecurity, it is mostly unstructured and unlabeled which makes it difficult to process effectively. Businesses and governments alike solve this problem by using machine learning algorithms to characterize the data and make decisions with it. However, conventional machine learning processes consume excessive computational resources and time: one of the most prominent, K-means clustering, has an approximate time complexity of O(n^2), where n is the input data size. This quadratic time complexity causes scalability problems with large datasets. In this project, I have created an improved, more scalable clustering algorithm by leveraging quantum computation. The approach (new Q-means) involves an Angle Embedding Feature Map, an d-dimensional SWAP Test, and a dynamic, threshold distance-based termination criteria. After implementing this algorithm using the IBM Qiskit SDK, the new Q-means algorithm was run several times on different dimensional datasets. On an average, the new Q-means performed 18% better than the K-means algorithm based on the Adjusted Rand Index. In terms of the simulation execution time, the new Q-means was about six times faster than the existing Q-means due to a multi-threaded implementation and faster convergence. The time complexity of the new Q-means without a Quantum Random Access Memory (QRAM) is O(n^2). While the existing Q-means algorithm, which utilizes QRAM, has a time complexity of O(n(log n)^p), the time complexity of the new Q-means with QRAM is significantly better—O(n).
Today computers are used to store data in memory and then process them. In our big data era, we are facing the challenge of storing and processing the data simply due to their fast ever growing size. Quantum computation offers solutions to these two prominent issues quantum mechanically and beautifully. Through careful design to employ superposition, entanglement, and interference of quantum states, a quantum algorithm can allow a quantum computer to store datasets of exponentially large size as linear size and then process them in parallel. Quantum computing has found its way in the world of machine learning where new ideas and approaches are in great need as the classical computers have reached their capacity and the demand for processing big data grows much faster than the computing power the classical computers can provide today. Nearest neighbor algorithms are simple, robust, and versatile supervised machine learning algorithms, which store all training data points as their learned “model” and make the prediction of a new test data point by computing the distances between the query point and all the training data points. Quantum counterparts of these classical algorithms provide efficient and elegant ways to deal with the two major issues of storing data in memory and computing the distances. The purpose of our study is to select two similar quantum nearest neighbor algorithms and use a simple dataset to give insight into how they work, highlight their quantum nature, and compare their performances on IBM’s quantum simulator.
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.
k-Nearest Neighbours (k-NN) is a widely used non-parametric, instance-based classification algorithm; however, its traditional implementation suffers from high computational cost, scalability limitations, and performance degradation in high-dimensional spaces. To address these challenges, this paper proposes a hybrid quantum-classical k-Nearest Neighbours (Qk-NN) model that integrates quantum feature encoding and quantum-assisted feature transformation with classical k-NN classification. The proposed approach is evaluated on the Pima Indians Diabetes Dataset using feature subsets of 5, 6, and 7 dimensions, selected due to quantum circuit scalability constraints. Quantum feature transformations are implemented through parameterized quantum circuits simulated on classical hardware in an ideal noiseless environment. Model performance is assessed using accuracy and log loss with a fixed Neighbourhood size of k = 5. Experimental results show that the Hybrid Qk-NN is superior to the classical k-NN in each feature subset. In particular, with five features, the Hybrid Qk-NN registers an accuracy of 77. 62 % while classical k-NN only achieves 71. 84 %, meanwhile, the loss values are quite lower. Quantum-assisted feature mapping capable of increasing the performance of classification is suggested by these results, and hybrid quantum-classical models are shown to be a viable bridge to the quantum machine learning world in the future.