Yuechi Ma

Ximing Wang, Yuechi Ma, Min-Hsiu Hsieh et al.

In classical machine learning, a set of weak classifiers can be adaptively combined to form a strong classifier for improving the overall performance, a technique called adaptive boosting (or AdaBoost). However, constructing the strong classifier for a large data set is typically resource consuming. Here we propose a quantum extension of AdaBoost, demonstrating a quantum algorithm that can output the optimal strong classifier with a quadratic speedup in the number of queries of the weak classifiers. Our results also include a generalization of the standard AdaBoost to the cases where the output of each classifier may be probabilistic even for the same input. We prove that the update rules and the query complexity of the non-deterministic classifiers are the same as those of deterministic classifiers, which may be of independent interest to the classical machine-learning community. Furthermore, the AdaBoost algorithm can also be applied to data encoded in the form of quantum states; we show how the training set can be simplified by using the tools of t-design. Our approach describes a model of quantum machine learning where quantum speedup is achieved in finding the optimal classifier, which can then be applied for classical machine-learning applications.

Yue-Chi Ma, Man-Hong Yung

Quantum information science has profoundly changed the ways we understand, store, and process information. A major challenge in this field is to look for an efficient means for classifying quantum state. For instance, one may want to determine if a given quantum state is entangled or not. However, the process of a complete characterization of quantum states, known as quantum state tomography, is a resource-consuming operation in general. An attractive proposal would be the use of Bell's inequalities as an entanglement witness, where only partial information of the quantum state is needed. The problem is that entanglement is necessary but not sufficient for violating Bell's inequalities, making it an unreliable state classifier. Here we aim at solving this problem by the methods of machine learning. More precisely, given a family of quantum states, we randomly picked a subset of it to construct a quantum-state classifier, accepting only partial information of each quantum state. Our results indicated that these transformed Bell-type inequalities can perform significantly better than the original Bell's inequalities in classifying entangled states. We further extended our analysis to three-qubit and four-qubit systems, performing classification of quantum states into multiple species. These results demonstrate how the tools in machine learning can be applied to solving problems in quantum information science.