Structuring quantum effects: superoperators as arrows

@article{Vizzotto2006StructuringQE,
  title={Structuring quantum effects: superoperators as arrows},
  author={Juliana Kaizer Vizzotto and Thorsten Altenkirch and Amr Sabry},
  journal={Mathematical Structures in Computer Science},
  year={2006},
  volume={16},
  pages={453 - 468}
}
We show that the model of quantum computation based on density matrices and superoperators can be decomposed into a pure classical (functional) part and an effectful part modelling probabilities and measurement. The effectful part can be modelled using a generalisation of monads called arrows. We express the resulting executable model of quantum computing in the Haskell programming language using its special syntax for arrow computations. However, the embedding in Haskell is not perfect: a… 
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References

SHOWING 1-10 OF 30 REFERENCES
Structure and interpretation of quantum mechanics: a functional framework
TLDR
It is concluded that functional languages are right tools for formal computations in quantum physics by constructing effectively the tensor states for composed systems and a toy model of quantum circuit toolbox.
Functional Quantum Programming
TLDR
This paper sees quantum programming as a special kind of non-deterministic programming where negative probabilities are allowed and a monadic style of quantum programming is proposed.
A functional quantum programming language
  • Jonathan Grattage
  • Computer Science
    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.
Modeling quantum computing in Haskell
The paper develops a model of quantum computing from the perspective of functional programming. The model explains the fundamental ideas of quantum computing at a level of abstraction that is
Quantum circuits with mixed states
TLDR
A solution for the subroutine problem: the general function that a quantum circuit outputs is a probabilistic function, but using pure state language, such a function can not be used as a black box in other computations.
A Lambda Calculus for Quantum Computation with Classical Control
TLDR
A functional programming language for quantum computers by extending the simply-typed lambda calculus with quantum types and operations, and gives a type system using affine intuitionistic linear logic.
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.
Quantum typing
The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda-calculus for the QRAMmodel, following the work of P. Selinger (2003) on quantum
Quantum Computation, Categorical Semantics and Linear Logic
TLDR
A type theory and denotational semantics are developed and provided for a simple fragment of the quantum lambda calculus, a formal language for quantum computation based on linear logic.
Quantum computation and quantum information
  • T. Paul
  • Physics
    Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal
...
...