Abstract Supervised machine learning is a popular approach to the solution of many real‐life problems. This approach is characterized by the use of labeled datasets to train algorithms for classifying data or predicting outcomes accurately. The question of the extent to which quantum computation can help improve existing classical supervised learning methods is the subject of intense research in the area of quantum machine learning. The debate centers on whether an advantage can be achieved already with current noisy quantum computer prototypes or it is strictly dependent on the full power of a fault‐tolerant quantum computer. The current proposals can be classified into methods that can be suitably implemented on near‐term quantum computers but are essentially empirical, and methods that use quantum algorithms with a provable advantage over their classical counterparts but only when implemented on the still unavailable fault‐tolerant quantum computer. It turns out that, for the latter class, the benefit offered by quantum computation can be shown rigorously using quantum kernels, whereas the approach based on near‐term quantum computers is very unlikely to bring any advantage if implemented in the form of hybrid algorithms that delegate the hard part (optimization) to the far more powerful classical computers.
Abstract Supervised machine learning is a popular approach to the solution of many real‐life problems. This approach is characterized by the use of labeled datasets to train algorithms for classifying data or predicting outcomes accurately. The question of the extent to which quantum computation can help improve existing classical supervised learning methods is the subject of intense research in the area of quantum machine learning. The debate centers on whether an advantage can be achieved already with current noisy quantum computer prototypes or it is strictly dependent on the full power of a fault‐tolerant quantum computer. The current proposals can be classified into methods that can be suitably implemented on near‐term quantum computers but are essentially empirical, and methods that use quantum algorithms with a provable advantage over their classical counterparts but only when implemented on the still unavailable fault‐tolerant quantum computer. It turns out that, for the latter class, the benefit offered by quantum computation can be shown rigorously using quantum kernels, whereas the approach based on near‐term quantum computers is very unlikely to bring any advantage if implemented in the form of hybrid algorithms that delegate the hard part (optimization) to the far more powerful classical computers.
With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum circuit. While such "quantum models" are sometimes called "quantum neural networks", it has been repeatedly noted that their mathematical structure is actually much more closely related to kernel methods: they analyse data in high-dimensional Hilbert spaces to which we only have access through inner products revealed by measurements. This technical manuscript summarises and extends the idea of systematically rephrasing supervised quantum models as a kernel method. With this, a lot of near-term and fault-tolerant quantum models can be replaced by a general support vector machine whose kernel computes distances between data-encoding quantum states. Kernel-based training is then guaranteed to find better or equally good quantum models than variational circuit training. Overall, the kernel perspective of quantum machine learning tells us that the way that data is encoded into quantum states is the main ingredient that can potentially set quantum models apart from classical machine learning models.
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 use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits.
In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of research falls under the umbrella of quantum machine learning, a research area of computer science which has recently received wide attention. In particular, we investigate to what extent quantum computers can be used to accelerate supervised machine learning algorithms. The aim of this is to develop a clear understanding of the promises and limitations of the current state of the art of quantum algorithms for supervised machine learning, but also to define directions for future research in this exciting field. We start by looking at supervised quantum machine learning (QML) algorithms through the lens of statistical learning theory. In this framework, we derive novel bounds on the computational complexities of a large set of supervised QML algorithms under the requirement of optimal learning rates. Next, we give a new bound for Hamiltonian simulation of dense Hamiltonians, a major subroutine of most known supervised QML algorithms, and then derive a classical algorithm with nearly the same complexity. We then draw the parallels to recent "quantum-inspired" results, and will explain the implications of these results for quantum machine learning applications. Looking for areas which might bear larger advantages for QML algorithms, we finally propose a novel algorithm for Quantum Boltzmann machines, and argue that quantum algorithms for quantum data are one of the most promising applications for QML with potentially exponential advantage over classical approaches.
With near-term devices available and the race for fault-tolerant computers in full swing, researchers became interested in the question of what happens if we replace a machine learning model with a circuit. While such quantum are sometimes called quantum neural networks, it has been repeatedly noted that their mathematical structure is actually much more closely related to kernel methods: they analyse data in high-dimensional Hilbert spaces to which we only have access through inner products revealed by measurements. This technical manuscript summarises, formalises and extends the link by systematically rephrasing models as a kernel method. It shows that most near-term and fault-tolerant models can be replaced by a general support vector machine whose kernel computes distances between data-encoding states. In particular, kernel-based training is guaranteed to find better or equally good models than variational circuit training. Overall, the kernel perspective of machine learning tells us that the way that data is encoded into states is the main ingredient that can potentially set models apart from classical machine learning models.
Abstract With quantum computing technologies nearing the era of commercialization and quantum supremacy, machine learning (ML) appears as one of the promising ‘killer’ applications. Despite significant effort, there has been a disconnect between most quantum ML proposals, the needs of ML practitioners, and the capabilities of near-term quantum devices to demonstrate quantum enhancement in the near future. In this contribution to the focus collection ‘What would you do with 1000 qubits?’, we provide concrete examples of intractable ML tasks that could be enhanced with near-term devices. We argue that to reach this target, the focus should be on areas where ML researchers are struggling, such as generative models in unsupervised and semi-supervised learning, instead of the popular and more tractable supervised learning techniques. We also highlight the case of classical datasets with potential quantum-like statistical correlations where quantum models could be more suitable. We focus on hybrid quantum–classical approaches and illustrate some of the key challenges we foresee for near-term implementations. Finally, we introduce the quantum-assisted Helmholtz machine (QAHM), an attempt to use near-term quantum devices to tackle high-dimensional datasets of continuous variables. Instead of using quantum computers to assist deep learning, as previous approaches do, the QAHM uses deep learning to extract a low-dimensional binary representation of data, suitable for relatively small quantum processors which can assist the training of an unsupervised generative model. Although we illustrate this concept on a quantum annealer, other quantum platforms could benefit as well from this hybrid quantum–classical framework.