Resource theory of quantum scrambling

Abstract

Quantum computers are devices which one can use to perform computations by exploiting the principles of quantum mechanics. One such principle is scrambling, which describes the spread of local information throughout a quantum system. In this dissertation, we introduce a framework, known as a resource theory, to mathematically define and measure scrambling. We show its connec- tion to several topics in quantum information. Among them, we show that scrambling results in training obstacles in an area of quantum computation known as quantum machine learning. We use our framework to explain recent experimental results, in which scientists at Google used scram- bling to measure the source of computational speed-ups using their quantum processor. Our theory provides an approach to study quantum chaos and its applications to quantum computation.