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- Thorsten Altenkirch, Jonathan Grattage
- 20th Annual IEEE Symposium on Logic in Computer…
- 2005

We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive semantics of irreversible quantum computations realisable as quantum gates. QML… (More)

We introduce a compiler for the functional quantum programming language QML [1], developed in Haskell. The compiler takes QML expressions as input and outputs a representation of quantum circuits (via the category FQC of finite quantum computations) which can be simulated by the simulator presented here, or by using a standard simulator for quantum gates.… (More)

- Thorsten Altenkirch, Jonathan Grattage, Juliana Kaizer Vizzotto, Amr Sabry
- Electr. Notes Theor. Comput. Sci.
- 2007

We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously developed denotational semantics of QML. The completeness proof also gives rise to a normalisation algorithm following the normalisation-by-evaluation approach. The current… (More)

- Jonathan Grattage
- Electr. Notes Theor. Comput. Sci.
- 2011

This paper gives an introduction to and overview of the functional quantum programming language QML. The syntax of this language is defined and explained, along with a new QML definition of the quantum teleport algorithm. The categorical operational semantics of QML is also briefly introduced, in the form of annotated quantum circuits. This definition leads… (More)

We introduce the language QML, a functional language for quantum computations on finite types. QML introduces quantum data and control structures, and integrates reversible and irreversible quantum computation. QML is based on strict linear logic, hence weakenings, which may lead to decoherence, have to be explicit. We present an operational semantics of… (More)

- Pablo Arrighi, Jonathan Grattage
- J. Comput. Syst. Sci.
- 2012

We describe an n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA then correspond to one step of the simulated QCA. The simulation… (More)

- Pablo Arrighi, Jonathan Grattage
- Natural Computing
- 2011

There have been several non-axiomatic approaches taken to define quantum cellular automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work we show that any QCA can be put into the form of a PQCA. Our construction reconciles all the non-axiomatic definitions of QCA, showing that they can all simulate one… (More)

- Pablo Arrighi, Jonathan Grattage
- LATA
- 2010

- Alejandro Díaz-Caro, Pablo Arrighi, Manuel Gadella, Jonathan Grattage
- Electr. Notes Theor. Comput. Sci.
- 2011

This paper demonstrates how to add a measurement operator to quantum λ-calculi. A proof of the consistency of the semantics is given through a proof of confluence presented in a sufficiently general way to allow this technique to be used for other languages. The method described here may be applied to probabilistic rewrite systems in general, and to add… (More)

In the quest to develop a quantum programming language, quantum extensions of functional languages give a very promising route, hence the explosion of works on quantum lambda calculi and quantum functional languages [1, 4, 9, 10]. Roughly, one could say that the current language proposals can be split into two categories. In the rst category the qubits are… (More)