| Summary: | The goal of this thesis is to explore the extent and limitations of existing techniques for the verification and validation of quantum systems, and to develop new techniques that are: (i) more efficient; (ii) mathematically rigorous; and (iii) practically implementable. We give a survey of contemporary techniques and protocols for the verification and characterisation of quantum states and processes, before deriving efficient protocols of our own. We construct an optimally efficient protocol constructed from local measurements for verifying that the output of an experiment agrees with a known target state, for both two-qubit and stabilizer states. We then show that this protocol is also optimal for the task of estimating the fidelity to a known target state, and to analyse its effectiveness we run both the optimal protocol and its closest competitors on a silicon-based photonic chip designed to produce arbitrary two-qubit states. We discuss the validation of quantum systems in two contexts. Firstly, we validate a quantum computational advantage over classical computers when faced with the task of producing solutions to differential equations via the finite element method. Secondly, we provide a blueprint for the validation of quantum effects in general relativistic systems, by outlining a space-based experiment designed to test the interplay between the two theories.
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