Theory of Quantum System Certification

The precise control of complex quantum systems promises numerous technological applications including digital computing. complexity such devices renders the certification their correct functioning a challenge. To address this challenge, methods were developed in last decade. In tutorial, we explain prominent protocols for certifying physical layer described by states and processes. Such are particularly important development near-term devices. Specifically, discuss direct state certification, fidelity estimation, shadow process randomized benchmarking cross-entropy benchmarking. Moreover, provide an introduction to powerful mathematical methods, which widely used information theory, order derive theoretical guarantees protocols.