An applied quantum Hoare logic

We derive a variant of quantum Hoare logic (QHL), called applied quantum Hoare logic (aQHL for short), by: 1. restricting QHL to a special class of preconditions and postconditions, namely projections, which can significantly simplify verification of quantum programs and are much more convenient when used in debugging and testing; and 2. adding several rules for reasoning about robustness of quantum programs, i.e. error bounds of outputs. The effectiveness of aQHL is shown by its applications to verify two sophisticated quantum algorithms: HHL (Harrow-Hassidim-Lloyd) for solving systems of linear equations and qPCA (quantum Principal Component Analysis).