Connecting Quantum Proof Systems and Hoare Logic

Overview & Synopsis

Verifying quantum programs today requires specialized proof systems built on interactive theorem provers such as Rocq, Lean, Isabelle, or Why3, and even modest quantum algorithms cost substantial human effort to verify. Because quantum programs cannot be effectively checked by runtime testing, formal verification is the only viable path to correctness, making the cost of these bespoke systems the chief barrier to scalable quantum software assurance. We show that verifying a quantum program should be no harder than verifying a classical array program, a paradigm commonly used in parallel programming: the Qafny quantum proof system translates into Hoare logic with array theory completely (every Qafny proof becomes a valid Hoare triple) and soundly (a valid translated triple certifies only true quantum specifications), and we mechanize the completeness direction in Rocq. The embedding determinizes quantum proof obligations and exposes the full machinery of classical automated verifiers (e.g. Dafny and SMT-based separation logic) to quantum code, removing the need for dedicated quantum proof system infrastructure. In particular, the embedding supplies the correctness argument that the existing compilation of Qafny into Dafny lacks.