Understand
Learning about physical systems from quantum-enhanced experiments, relying on a quantum memory and quantum processing, can outperform learning from experiments in which only classical memory and processing are available.
- Whereas quantum advantages have been established for a variety of state learning tasks, quantum process learning allows for comparable advantages only with a careful problem formulation and is less understood.
- We establish an exponential quantum advantage for learning an unknown $n$-qubit quantum process $\mathcal{N}$.
- We show that a quantum memory allows to efficiently solve the following tasks: (a) learning the Pauli transfer matrix of an arbitrary $\mathcal{N}$, (b) predicting expectation values of bounded Pauli-sparse observables measured on the output of an arbitrary $\mathcal{N}$ upon input of a Pauli-sparse state, and (c) predicting expectation values of arbitrary bounded observables measured on the output of an unknown $\mathcal{N}$ with sparse Pauli transfer matrix upon input of an arbitrary state.