Learning quantum states from their classical shadows

In quantum mechanics, a quantum many-body system is represented by a large complex matrix whose size scales exponentially with the number of particles. This intrinsic exponential complexity empowers quantum technologies but, at the same time, it makes it practically impossible to completely characterize, or learn, a quantum many-body system even of moderate size (the current limit of quantum tomography being 40–50 qubits). This is an issue given that learning quantum systems is central to the development of quantum technologies.