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Quantum Weakest Preconditions
Ellie D'Hondt, Prakash Panangaden
abstract: We develop a notion of predicate transformer and, in particular, the weakest
precondition, appropriate for quantum computation. We show that there is a
Stone-type duality between the usual state-transformer semantics and the
weakest precondition semantics. Rather than trying to reduce quantum
computation to probabilistic programming we develop a notion that is directly
taken from concepts used in quantum computation. The proof that weakest
preconditions exist for completely positive maps follows immediately from the
Kraus representation theorem. As an example we give the semantics of Selinger's
language in terms of our weakest preconditions. We also cover some specific
situations and exhibit an interesting link with stabilizers.
- oai_identifier:
- oai:arXiv.org:quant-ph/0501157
- categories:
- quant-ph
- comments:
- 24 pages, 3 figures. Substantial rewrite based on referee reports
- arxiv_id:
- quant-ph/0501157
- journal_ref:
- Mathematical Structures in Computer Science, 2006
- created:
- 2005-01-26
- updated:
- 2006-02-23
Full article ▸
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