209 research outputs found
Local Reasoning about Probabilistic Behaviour for Classical-Quantum Programs
Verifying the functional correctness of programs with both classical and
quantum constructs is a challenging task. The presence of probabilistic
behaviour entailed by quantum measurements and unbounded while loops complicate
the verification task greatly. We propose a new quantum Hoare logic for local
reasoning about probabilistic behaviour by introducing distribution formulas to
specify probabilistic properties. We show that the proof rules in the logic are
sound with respect to a denotational semantics. To demonstrate the
effectiveness of the logic, we formally verify the correctness of non-trivial
quantum algorithms including the HHL and Shor's algorithms.Comment: 27 pages. arXiv admin note: text overlap with arXiv:2107.0080
Quantum Hoare logic with classical variables
Hoare logic provides a syntax-oriented method to reason about program
correctness, and has been proven effective in the verification of classical and
probabilistic programs. Existing proposals for quantum Hoare logic either lack
completeness or support only quantum variables, thus limiting their capability
in practical use.
In this paper, we propose a quantum Hoare logic for a simple while language
which involves both classical and quantum variables. Its soundness and relative
completeness are proven for both partial and total correctness of quantum
programs written in the language. Remarkably, with novel definitions of
classical-quantum states and corresponding assertions, the logic system is
quite simple and similar to the traditional Hoare logic for classical programs.
Furthermore, to simplify reasoning in real applications, auxiliary proof rules
are provided which support the introduction of disjunction and quantifiers in
the classical part of assertions, and of super-operator application and
superposition in the quantum part. Finally, a series of practical quantum
algorithms, in particular the whole algorithm of Shor's factorisation, are
formally verified to show the effectiveness of the logic
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
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