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Self-Testing of One-Qubit Gates

We design self-testers for several families of unitary one-qubit gates, in particular for the family of Hadamard gates. A self-tester for a gate family F is a classical procedure which, given a gate G, decides with high probability if G is close, with respect to some norm, to an element of F . For this the self-tester can access the gate G only in a restricted way: it can measure in the computational basis the outcome of iterating G on the ‘classical’ basis states. To achieve our goal we borrow an idea of the theory of program testing: we characterize the gate families by specific properties. Then we develop a theory of robustness for these properties and show that they lead to self-testers.