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 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.
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, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge is that machine learning with the rapidly growing "big data" could become intractable for classical computers. Recently, quantum machine learning algorithms [Lloyd, Mohseni, and Rebentrost, arXiv.1307.0411] were proposed which could offer an exponential speedup over classical algorithms. Here, we report the first experimental entanglement-based classification of two-, four-, and eight-dimensional vectors to different clusters using a small-scale photonic quantum computer, which are then used to implement supervised and unsupervised machine learning. The results demonstrate the working principle of using quantum computers to manipulate and classify high-dimensional vectors, the core mathematical routine in machine learning. The method can, in principle, be scaled to larger numbers of qubits, and may provide a new route to accelerate machine learning.
Quantum machine learning (QML) provides a transformative approach to data analysis by integrating the principles of quantum computing with classical machine learning methods. With the exponential growth of data and the increasing complexity of computational tasks, quantum algorithms offer tremendous advantages in terms of processing speed, memory efficiency, and the ability to resolve issues intractable for classical systems. In this work, the use of QML techniques for both supervised and unsupervised learning problems is explored. Quantum-enhanced models such Quantum Support Vector Machines (QSVMs) and Quantum Neural Networks (QNNs) show outstanding performance in classification and regression tasks by using quantum kernels and entanglement in supervised learning. Moreover, hybrid quantum-classical solutions offer useful implementations on noisy intermediate-scale quantum (NISQ) devices, hence bridging the gap between present quantum technology and practical uses. By means of comparative analysis, this paper emphasizes the possible benefits and drawbacks of QML, thereby providing understanding of its future importance in sectors including material science, finance, and healthcare. In the end, QML opens the path for a new era of intelligent data processing and solves until unthinkable difficult challenges.
Machine Learning or Artificial Intelligence basically involves tasks of modifying and supervising problems taken as vectors in multi-dimensional space. The Primitive algorithms which are used take Polynomial Time for computing such vector problems which are not fruitful for us, on the other hand, Quantum algorithms have the capability to solve such vector problems in a considerable amount of time by using Quantum-Mechanical operations. For example, we can perform a Database Search in a time which is Quadratic-ally faster than the primitive search algorithm. Quantum Algorithms rely on Quantum physics and therefore the algorithms are Incoherent in nature and this property makes them more interesting to study. In this paper, we provide the insights of Quantum Machine Learning and we formally prove that the Execution Time of the algorithm is greatly optimized with the help of Adiabatic Quantum Learning. Also, we prove that Quantum Associative Memories can store exponentially more data than its primitive counterparts. Data mining concept is very similar to Machine Learning and we will also show how QML will be beneficial in such cause as well.
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.