Precise control over complex quantum systems on scales out of reach of classical simulations hold promises for many scientific and technological applications. With the advent of these novel technologies comes the necessity for characterizing their functioning. The precise understanding of the inner-working of quantum devices is a particularly daunting task in the interesting regime of high complexity, easily exhausting time and memory of classical computers in the pre- and post-processing. In addition, inaccuracy in the implementation of the measurement apparatus reduces the achievable precision of characterization protocols. Our work introduces new semi-device-dependent quantum system identification protocols. These are protocols for identifying the abstract description of a quantum device, as being in a certain quantum state, implementing a quantum process or being governed by a specific Hamiltonian time-evolution. The protocols are designed to exhibit robustness against imperfections in the measurement apparatus and to efficiently exploit structural assumptions on the quantum system that reduce the resource requirements. In particular, we present results on the identification of a low-rank quantum state from measurements taken with a partially uncalibrated measurement device, the identification of a unitary quantum process from data that is robust against imperfections in the state preparation and measurement and the high-precision and robust identification of non-interacting Hamiltonians in an analogue quantum simulation. We report on rigorous mathematical guarantees for the protocols that delineate their realm of applicability in practice as well as numerical performance evaluations and experimental demonstrations. Occasionally, the development of technical methods will bring us to further applications and questions outside of the field of quantum characterization, such as the nature of the sign problem arising in the classical Monte-Carlo simulations of quantum systems.
