Presents a Hoare logic for quantum programs with classical variables using paired classical first-order formulas and quantum predicates, plus a simplified proof system with minimal modifications to classical Hoare logic.
Selinger, Towards a quantum programming language, Mathematical Structures in Computer Science 14(2004) 527-586
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A Practical Quantum Hoare Logic with Classical Variables, I
Presents a Hoare logic for quantum programs with classical variables using paired classical first-order formulas and quantum predicates, plus a simplified proof system with minimal modifications to classical Hoare logic.