Understanding the role of data and quantum memory in a quantum learning landscape

If we believe both that quantum computers may be able to do some computations exponentially faster than their classical counterparts and that we live in a quantum world, then our ability to learn from observational data as scientists may fundamentally change what we can do. Here, we will first review some recent results in quantum machine learning that allow us to put these ideas on a rigorous footing. We then show that quantum computers, and more specifically quantum memory, offer us an opportunity to learn from a quantum world with exponentially less data than traditional experiments. This exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. We then give an outlook on this technology and challenges that we face in expanding the reach of quantum technology in learning.