Many scientific advancements in physics and chemistry depend on our ability to learn and make predictions in a quantum-mechanical world. In this talk, I will review recent advances in understanding what we could learn from quantum experiments and how efficient could we be. I will present results showing that sometimes we could make reliable predictions using much fewer experiments than one may expect and provide relevant problems that are actually impossible to learn. Finally, I will give rigorous statements showing how the development of quantum technology, including a combination of quantum sensors, quantum memory, and quantum computers, could significantly enhance our ability to learn and predict.

The talk will cover results from collaborations with John Preskill, Richard Kueng, Jordan Cotler, Sitan Chen, Jerry Li, Jarrod McClean, Michael Broughton, Steve Flammia, and others.