Maria Schuld
Machine learning and quantum computing mathematical foundations are strikingly similar.
——Nature
Machine learning and quantum computing are two technologies that each have the potential to alter how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous in pattern recognition, with support vector machines (SVMs) being the best known method for classification problems. However, there are limitations to the successful solution to such classification problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element in the computational speed-ups enabled by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference.
机器学习
何为支持向量机？
In machine learning, so-called kernel methods are a well-established field with a surprisingly similar logic. The idea of kernel methods is to formally embed data into a higher-dimensional feature space in which it becomes easier to analyse (see Figure 1). A popular example is a support vector machine that draws a decision boundary between two classes of data points by mapping the data into a feature space where it becomes linearly separable.
In a nutshell, kernel methods carry out machine learning by defining which data points are similar to each other and which are not. Mathematically speaking, similarity is a distance in data space — that is, a distance between the representations of data points as numbers.
量子机器学习
Quantum-enhanced machine learning
Havlíček et al. demonstrate how quantum computers could improve the performance of machine-learning algorithms. In this simple illustration, a conventional (classical) computer uses machine learning to classify images of animals. Images whose pixels contain similar colours are positioned close together in data space. The classical computer sends these data to a quantum computer that maps each of the images to a particular quantum state in a space of such states. Images that are close together in data space, but are different in content, are represented by states that are far apart in quantum space. The quantum computer sends the distances between the quantum states to the classical computer to improve the image classification.
