  Quantum technology has the potential to revolutionize how we acquire and
process experimental data to learn about the physical world. An experimental
setup that transduces data from a physical system to a stable quantum memory,
and processes that data using a quantum computer, could have significant
advantages over conventional experiments in which the physical system is
measured and the outcomes are processed using a classical computer. We prove
that, in various tasks, quantum machines can learn from exponentially fewer
experiments than those required in conventional experiments. The exponential
advantage holds in predicting properties of physical systems, performing
quantum principal component analysis on noisy states, and learning approximate
models of physical dynamics. In some tasks, the quantum processing needed to
achieve the exponential advantage can be modest; for example, one can
simultaneously learn about many noncommuting observables by processing only two
copies of the system. 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.
Our results highlight how quantum technology can enable powerful new strategies
to learn about nature.
