Floyd--hoare logic for quantum programs

@article{Ying2012FloydhoareLF,
  title={Floyd--hoare logic for quantum programs},
  author={Mingsheng Ying},
  journal={ACM Trans. Program. Lang. Syst.},
  year={2012},
  volume={33},
  pages={19:1-19:49}
}
  • M. Ying
  • Published 1 December 2011
  • Computer Science
  • ACM Trans. Program. Lang. Syst.
Floyd--Hoare logic is a foundation of axiomatic semantics of classical programs, and it provides effective proof techniques for reasoning about correctness of classical programs. To offer similar techniques for quantum program verification and to build a logical foundation of programming methodology for quantum computers, we develop a full-fledged Floyd--Hoare logic for both partial and total correctness of quantum programs. It is proved that this logic is (relatively) complete by exploiting… 
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References

SHOWING 1-10 OF 48 REFERENCES
Proof rules for the correctness of quantum programs
TLDR
The notion of quantum predicate proposed by D'Hondt and Panangaden is applied to analyze a simple language fragment which may describe the quantum part of a future quantum computer in Knill's architecture and the proof rules are extended to be complete in the sense that any correct assertion about the quantum loops can be proved.
The Logic of Quantum Programs
TLDR
A dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound quantum systems is introduced and a sound proof system for this logic is presented.
Reasoning About Imperative Quantum Programs
TLDR
The state logic is used to provide a sound Hoare-style calculus for quantum imperative programs and the calculus is illustrated by proving the correctness of the Deutsch algorithm.
Quantum weakest preconditions
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…
Quantum Programming
TLDR
The theory of quantum programming provides tools to write both classical and quantum specifications, develop quantum programs that implement these specifications, and reason about their comparative time and space complexity all in the same framework.
Towards a quantum programming language
  • P. Selinger
  • Computer Science
    Mathematical Structures in Computer Science
  • 2004
TLDR
This paper describes the syntax and semantics of a simple quantum programming language with high-level features such as loops, recursive procedures, and structured data types, and has an interesting denotational semantics in terms of complete partial orders of superoperators.
A functional quantum programming language
  • Jonathan Grattage
  • Mathematics, Physics
    20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
  • 2005
TLDR
QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings explicit, and preserves superpositions and entanglement -which is essential for quantum parallelism.
LQP: the dynamic logic of quantum information
  • A. Baltag, S. Smets
  • Computer Science, Physics
    Mathematical Structures in Computer Science
  • 2006
TLDR
A dynamic logic formalism for reasoning about information flow in composite quantum systems, capable of expressing important features of quantum measurements and unitary evolutions of multi-partite states, as well as giving logical characterisations to various forms of entanglement.
Dynamic Quantum Logic for Quantum Programs
TLDR
A way to apply quantum logic to the study of quantum programs is presented by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly.
Soundness and Completeness of an Axiom System for Program Verification
  • S. Cook
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1978
TLDR
The main new results are the completeness theorem, and a careful treatment of the procedure call rules for procedures with global variables in their declarations.
...
1
2
3
4
5
...