# Dynamic Quantum Logic for Quantum Programs

@article{Brunet2003DynamicQL, title={Dynamic Quantum Logic for Quantum Programs}, author={Olivier Brunet and Philippe Jorrand}, journal={International Journal of Quantum Information}, year={2003}, volume={02}, pages={45-54} }

We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way, the evolution of the system becomes part of the logical study. We show how both unitary operations and two-valued measurements can be included in this formalism and can thus be handled logically.

## 57 Citations

The Logic of Quantum Programs

- Computer Science, PhysicsArXiv
- 2021

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.

A Logic for Formal Verification of Quantum Programs

- Computer ScienceASIAN
- 2009

This paper provides a Hoare-style logic for quantum computation that proves properties of well-known algorithms and is an extension of the probabilistic Hoare -style logic defined by den Hartog.

Quantum programming: From theories to implementations

- Computer Science
- 2012

This paper surveys the new field of programming methodology and techniques for future quantum computers, including design of sequential and concurrent quantum programming languages, their semantics…

Toward automatic verification of quantum programs

- Computer ScienceFormal Aspects of Computing
- 2018

This paper summarises the results obtained by the author and his collaborators in a program logic approach to the verification of quantum programs, including quantum Hoare logic, invariant generation…

A Logic for Recursive Quantum Programs

- Computer ScienceArXiv
- 2018

This paper presents a logic for recursive quantum programs, an extension of quantum Hoare logic for quantum While-programs, and its effectiveness is shown by a running example: fixed-point Grover's search.

Quantum Temporal Logic

- PhilosophyArXiv
- 2019

A model of quantum concurrent program is introduced, which can be used to model the behaviour of reactive quantum systems and to design quantum compilers, and a quantum Bohm-Jacopini theorem is proved which states that any such program is equivalent to a Q-While program.

A Quantum Interpretation of Bunched Logic & Quantum Separation Logic

- Philosophy, Physics2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2021

A model of the substructural logic of Bunched Implications that is suitable for reasoning about quantum states and develops a program logic where pre- and post-conditions are BI formulas describing quantum states.

Hoare Logic for Quantum Programs

- Computer Science
- 2009

It is proved that this logic is (relatively) complete by exploiting the power of weakest preconditions and weakest liberal precondition for quantum programs.

Representation Systems, Orthoposets and Quantum Logic

- Computer Science
- 2004

A special form of these structures is used to define a method for decomposing orthoposets into boolean algebras, in such a way that it permits to consider more properties about a quantum system than using usual methods.

Quantum programming languages: survey and bibliography

- Computer ScienceMathematical Structures in Computer Science
- 2006

The study of quantum Programming languages is justified, the basics of quantum computing are presented, the literature in quantum programming languages is surveyed, and directions for future research are indicated.

## References

SHOWING 1-10 OF 15 REFERENCES

Quantum gates and circuits

- PhysicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 1998

A historical review is given of the emergence of the idea of the quantum logic gate from the theory of reversible Boolean gates. I highlight the quantum XOR or controlled NOT as the fundamental…

Can Quantum-Mechanical Description of Physical Reality be Considered Complete?

- Physics
- 1935

It is shown that a certain "criterion of physical reality" formulated in a recent article with the above title by A. Einstein, B. Podolsky and N. Rosen contains an essential ambiguity when it is…

Quantum Logic

- ArtDiscrete mathematics and theoretical computer science
- 1998

When reading the PDF, the author is very reliable in using the words to create sentences, and the ways how the author creates the diction to influence many people will be seen.

The Logic of Quantum Mechanics

- Philosophy
- 1936

One of the aspects of quantum theory which has attracted the most general attention, is the novelty of the logical notions which it presupposes. It asserts that even a complete mathematical…

On the Foundations of Quantum Physics

- Physics
- 1976

The interpretation of quantum theory has always been a source of difficulties, especially with regard to the theory of measurement. We do not intend to enter here into the details of the polemic…

Elementary gates for quantum computation.

- MathematicsPhysical review. A, Atomic, molecular, and optical physics
- 1995

U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits.

Quantum Computation and Quantum Information

- Physics, Computer Science
- 2000

This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

The Structure and Interpretation of Quantum Mechanics

- Physics
- 1989

Preface Introduction. The Stern-Gerlach Experiment PART I THE STRUCTURE OF QUANTUM THEORY 1. Vector Spaces Vectors Operators Eigenvectors and Eigenvalues Inner Products of Vectors in R2 Complex…

Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.

- PhysicsPhysical review letters
- 1993

An unknown quantum state \ensuremath{\Vert}\ensuremath{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen…