Quantum algorithms are being extensively researched nowadays, seeing the potential to provide exponential speedup compared to classical algorithm execution. This speedup can play a significant role in machine learning, where training a model is usually prolonged. Training a machine learning model requires compressing large vectors into small computational units, and quantum computers inherently are fast at compressing the large vectors into small computations and tensor products. The present work aims to compare the K-means, a classical machine learning algorithm, and Q-means, a Quantum algorithm. Here in this work, we use q-means, a quantum algorithm for clustering, a canonical problem in unsupervised machine learning. The q-means algorithm has convergence and precision guarantees similar to k-means. [14]It outputs with high probability a good approximation of the k cluster centroids like the classical algorithm. The experimental results are demonstrated, which show a significant difference between k-means and q-means algorithms.
Quantum algorithms are being extensively researched nowadays, seeing the potential to provide exponential speedup compared to classical algorithm execution. This speedup can play a significant role in machine learning, where training a model is usually prolonged. Training a machine learning model requires compressing large vectors into small computational units, and quantum computers inherently are fast at compressing the large vectors into small computations and tensor products. The present work aims to compare the K-means, a classical machine learning algorithm, and Q-means, a Quantum algorithm. Here in this work, we use q-means, a quantum algorithm for clustering, a canonical problem in unsupervised machine learning. The q-means algorithm has convergence and precision guarantees similar to k-means. [14]It outputs with high probability a good approximation of the k cluster centroids like the classical algorithm. The experimental results are demonstrated, which show a significant difference between k-means and q-means algorithms.
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over the corresponding classical algorithms. In this paper, we introduce q-means, a new quantum algorithm for clustering which is a canonical problem in unsupervised machine learning. The q-means algorithm has convergence and precision guarantees similar to k-means, and it outputs with high probability a good approximation of the k cluster centroids like the classical algorithm. Given a dataset of Nd-dimensional vectors vi (seen as a matrix V∈RN×d) stored in QRAM, the running time of q-means is O(kdδ2ηκ(V)(μ(V)+kδη)+k2δ2η1.5κ(V)μ(V)) per iteration, where κ(V) is the condition number, μ(V) is a parameter that appears in quantum linear algebra procedures and η=maxi∣∣vi∣∣2. For a natural notion of well-clusterable datasets, the running time becomes O(k2dδ3η2.5+k2.5δ3η2) per iteration, which is linear in the number of features d, and polynomial in the rank k, the maximum square norm η and the error parameter δ. Both running times are only polylogarithmic in the number of datapoints N. Our algorithm provides substantial savings compared to the classical k-means algorithm that runs in time O(kdN) per iteration, particularly for the case of large datasets.
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over the corresponding classical algorithms. In this paper, we introduce q-means, a new quantum algorithm for clustering which is a canonical problem in unsupervised machine learning. The q-means algorithm has convergence and precision guarantees similar to k-means, and it outputs with high probability a good approximation of the k cluster centroids like the classical algorithm. Given a dataset of Nd-dimensional vectors vi (seen as a matrix V∈RN×d) stored in QRAM, the running time of q-means is O(kdδ2ηκ(V)(μ(V)+kδη)+k2δ2η1.5κ(V)μ(V)) per iteration, where κ(V) is the condition number, μ(V) is a parameter that appears in quantum linear algebra procedures and η=maxi∣∣vi∣∣2. For a natural notion of well-clusterable datasets, the running time becomes O(k2dδ3η2.5+k2.5δ3η2) per iteration, which is linear in the number of features d, and polynomial in the rank k, the maximum square norm η and the error parameter δ. Both running times are only polylogarithmic in the number of datapoints N. Our algorithm provides substantial savings compared to the classical k-means algorithm that runs in time O(kdN) per iteration, particularly for the case of large datasets.
Machine-learning tasks frequently involve problems of manipulating and classifying large numbers of vectors in high-dimensional spaces. Classical algorithms for solving such problems typically take time polynomial in the number of vectors and the dimension of the space. Quantum computers are good at manipulating high-dimensional vectors in large tensor product spaces. This paper provides supervised and unsupervised quantum machine learning algorithms for cluster assignment and cluster finding. Quantum machine learning can take time logarithmic in both the number of vectors and their dimension, an exponential speed-up over classical algorithms.
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the data, the computation time for training and using these statistical models grows quickly. Here, we propose and implement on the IBMQ a quantum analogue to K-means clustering, and compare it to a previously developed quantum support vector machine. We find the algorithm's accuracy comparable to the classical K-means algorithm for clustering and classification problems, and find that it becomes less computationally expensive to implement for large datasets as compared to its classical counterpart.
Quantum computing is one of the most promising solutions for solving optimization problems in the healthcare world. Quantum computing development aims to light up the execution of a vast and complex set of algorithmic instructions. For its implementation, the machine learning models are continuously evolving. Hence, the new challenge is to improve the existing complex and critical machine learning training models. Therefore, the healthcare sector is shifting from a classical to a quantum domain to sustain patient-oriented attention to healthcare patrons. This paper presents a hybrid classical-quantum approach for training the unsupervised data models. In order to achieve good performance and optimization of the machine learning algorithms, a quantum k-means (QK-means) clustering problem was deployed on the IBM quantum simulators, i.e.,the IBM QASM simulator. In the first place, the approach was theoretically studied and then implemented to analyze the experimental results. The approach was further tested using small synthetics and cardiovascular datasets on a qsam simulator to obtain the clustering solution. The future direction connecting the dots is the incremental k-means algorithm with the quantum platform, which would open hitherto unimaginable technological doors.
The exponential growth of data and the increasing complexity of high-dimensional classification problems have pushed classical computing methods to their limits. Quantum computing emerges as a promising paradigm to address these challenges. This research article explores advanced quantum algorithms for big data clustering and high-dimensional classification. We investigate quantum versions of K-means, spectral clustering, and support vector machines, comparing their performance with classical counterparts. Our results demonstrate significant speedups in processing time and improvements in clustering quality for high-dimensional datasets. Additionally, we propose a novel quantum-inspired classical algorithm that bridges the gap between quantum and classical approaches. This comprehensive study provides insights into the potential of quantum computing in revolutionizing data analysis and machine learning, paving the way for future advancements in the field.