A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where quantum computer may offer significant speedup. Several quantum algorithms for discriminative machine learning have been found based on efficient solving of linear algebraic problems, with potential exponential speedup in runtime under the assumption of effective input from a quantum random access memory. In machine learning, generative models represent another large class which is widely used for both supervised and unsupervised learning. Here, we propose an efficient quantum algorithm for machine learning based on a quantum generative model. We prove that our proposed model is exponentially more powerful to represent probability distributions compared with classical generative models and has exponential speedup in training and inference at least for some instances under a reasonable assumption in computational complexity theory. Our result opens a new direction for quantum machine learning and offers a remarkable example in which a quantum algorithm shows exponential improvement over any classical algorithm in an important application field.
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where quantum computer may offer significant speedup. Several quantum algorithms for discriminative machine learning have been found based on efficient solving of linear algebraic problems, with potential exponential speedup in runtime under the assumption of effective input from a quantum random access memory. In machine learning, generative models represent another large class which is widely used for both supervised and unsupervised learning. Here, we propose an efficient quantum algorithm for machine learning based on a quantum generative model. We prove that our proposed model is exponentially more powerful to represent probability distributions compared with classical generative models and has exponential speedup in training and inference at least for some instances under a reasonable assumption in computational complexity theory. Our result opens a new direction for quantum machine learning and offers a remarkable example in which a quantum algorithm shows exponential improvement over any classical algorithm in an important application field.
Quantum computing and artificial intelligence, combined together, may revolutionize future technologies. A significant school of thought regarding artificial intelligence is based on generative models. Here, we propose a general quantum algorithm for machine learning based on a quantum generative model. We prove that our proposed model is more capable of representing probability distributions compared with classical generative models and has exponential speedup in learning and inference at least for some instances if a quantum computer cannot be efficiently simulated classically. Our result opens a new direction for quantum machine learning and offers a remarkable example where a quantum algorithm shows exponential improvement over classical algorithms in an important application field.
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as to minimize the required number of features for achieving the learning to a desired accuracy. Here, we develop a quantum algorithm for sampling from this optimized distribution over features, in runtime O(D) that is linear in the dimension D of the input data. Our algorithm achieves an exponential speedup in D compared to any known classical algorithm for this sampling task. In contrast to existing quantum machine learning algorithms, our algorithm circumvents sparsity and low-rank assumptions and thus has wide applicability. We also show that the sampled features can be combined with regression by stochastic gradient descent to achieve the learning without canceling out our exponential speedup. Our algorithm based on sampling optimized random features leads to an accelerated framework for machine learning that takes advantage of quantum computers.
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.
The goal of generative machine learning is to model the probability distribution underlying a given data set. This probability distribution helps to characterize the generation process of the data samples. While classical generative machine learning is solely based on classical resources, generative quantum machine learning can also employ quantum resources - such as parameterized quantum channels and quantum operators - to learn and sample from the probability model of interest. Applications of generative (quantum) models are multifaceted. The trained model can generate new samples that are compatible with the given data and extend the data set. Additionally, learning a model for the generation process of a data set may provide interesting information about the corresponding properties. With the help of quantum resources, the respective generative models have access to functions that are difficult to evaluate with a classical computer and may improve the performance or lead to new insights. Furthermore, generative quantum machine learning can be applied to efficient, approximate loading of classical data into a quantum state which may help to avoid - potentially exponentially - expensive, exact quantum data loading. The aim of this doctoral thesis is to develop new generative quantum machine learning algorithms, demonstrate their feasibility, and analyze their performance. Additionally, we outline their potential application to efficient, approximate quantum data loading. More specifically, we introduce a quantum generative adversarial network and a quantum Boltzmann machine implementation, both of which can be realized with parameterized quantum circuits. These algorithms are compatible with first-generation quantum hardware and, thus, enable us to study proof of concept implementations not only with numerical quantum simulations but also real quantum hardware available today.
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessable way, and discusses the potential of a future theory of quantum learning.
Quantum machine learning (QML) is a computational paradigm that seeks to apply quantum-mechanical resources to solve learning problems. As such, the goal of this framework is to leverage quantum processors to tackle optimization, supervised, unsupervised and reinforcement learning, and generative modeling-among other tasks-more efficiently than classical models. Here we offer a high level overview of QML, focusing on settings where the quantum device is the primary learning or data generating unit. We outline the field's tensions between practicality and guarantees, access models and speedups, and classical baselines and claimed quantum advantages-flagging where evidence is strong, where it is conditional or still lacking, and where open questions remain. By shedding light on these nuances and debates, we aim to provide a friendly map of the QML landscape so that the reader can judge when-and under what assumptions-quantum approaches may offer real benefits.