Quantum advantages in learning unitary

Abstract

Quantum information and machine learning have achieved significant breakthroughs in the past decades and have an enormous potential for future technologies. Quantum machine learning explores the interaction between these two disciplines, making them benefit each other. One direction of research in quantum machine learning is the study of new learning tasks arising in quantum information processing. Such tasks include learning quantum states, e.g., state classification, and learning quantum processes, e.g., unitary gate learning. This dissertation presents an extensive study of the problem of learning unitary gates. In this problem, a machine is provided with an unknown unitary gate as training data, and the task is to reproduce the action of the target gate when the training gate is no longer accessible. We first focus on the internal memory in the learning machine. One fundamental question is whether a learning machine equipped with a quantum memory can perform better than any machine with only purely classical memories. A concrete example is presented here, showing that quantum memories can generally enhance the learning performance. This result is established by deriving the ultimate performance achievable with purely classical memories, thus providing a benchmark that can be used to experimentally demonstrate the implementation of quantum-enhanced learning. After establishing the benefit of quantum memories, we will explore the task of learning in the presence of noise. This task frequently arises in practice, but has never been considered in previous works, due to its technical challenges. Here we analyze a problem of noisy learning, discovering two surprising features. First, we find out that quantum techniques still allow us to retrieve the target unitary operation perfectly with some probability without knowing which learning gates are affected by noise. Second, we show that indefinite causal order can be used as a resource to increase the probability of correct learning. This dissertation further explores the application of the task of learning unitary gates to quantum communication and error correction. In this part, an optimal learning protocol is provided, which learns the misalignment information between two remote parties to allow them to communicate through noisy channels.