A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Reasoning about Grover's quantum search algorithm using probabilistic wp
ACM Transactions on Programming Languages and Systems (TOPLAS)
An axiomatic basis for computer programming
Communications of the ACM
The Science of Programming
Quantum computation and quantum information
Quantum computation and quantum information
A Discipline of Programming
Power Domains and Predicate Transformers: A Topological View
Proceedings of the 10th Colloquium on Automata, Languages and Programming
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
Towards a quantum programming language
Mathematical Structures in Computer Science
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
LQP: the dynamic logic of quantum information
Mathematical Structures in Computer Science
Journal of the ACM (JACM)
Quantum programming languages: survey and bibliography
Mathematical Structures in Computer Science
Distributed Measurement-based Quantum Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Commutativity of quantum weakest preconditions
Information Processing Letters
Proof rules for the correctness of quantum programs
Theoretical Computer Science
Programming with Quantum Communication
Electronic Notes in Theoretical Computer Science (ENTCS)
Natural Quantum Operational Semantics with Predicates
International Journal of Applied Mathematics and Computer Science - Selected Problems of Computer Science and Control
Generalised quantum weakest preconditions
Quantum Information Processing
Foundations of quantum programming
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
UC'11 Proceedings of the 10th international conference on Unconventional computation
Floyd--hoare logic for quantum programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
A logic for formal verification of quantum programs
ASIAN'09 Proceedings of the 13th Asian conference on Advances in Computer Science: information Security and Privacy
Reachability and termination analysis of concurrent quantum programs
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
Reachability probabilities of quantum markov chains
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
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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 stabilisers.