Results 1  10
of
20
A functional quantum programming language
 In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
, 2005
"... This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are inte ..."
Abstract

Cited by 46 (12 self)
 Add to MetaCart
This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits. The quantum circuit model is also given a formal categorical definition via the category FQC. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings, which may lead to the collapse of the quantum wavefunction, explicit. Strict programs are free from measurement, and hence preserve superpositions and entanglement. A denotational semantics of QML programs is presented, which maps QML terms
Probabilistic model–checking of quantum protocols
 DCM 2006: PROCEEDINGS OF THE 2ND INTERNATIONAL WORKSHOP ON DEVELOPMENTS IN COMPUTATIONAL MODELS
, 2005
"... We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communicati ..."
Abstract

Cited by 11 (6 self)
 Add to MetaCart
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using presentday technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of prism, a probabilistic modelchecking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniques by modelling a selection of quantum protocols (namely superdense coding, quantum teleportation, and quantum error correction) and verifying their basic correctness properties. Our results provide a foundation for further work on modelling and analysing larger systems such as those used for quantum cryptography, in which basic protocols are used as components.
The Quantum IO Monad
"... The Quantum IO monad is a purely functional interface to quantum programming implemented as a Haskell library. At the same time it provides a constructive semantics of quantum programming. The QIO monad separates reversible (i.e. unitary) and irreversible (i.e. probabilistic) computations and provid ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
The Quantum IO monad is a purely functional interface to quantum programming implemented as a Haskell library. At the same time it provides a constructive semantics of quantum programming. The QIO monad separates reversible (i.e. unitary) and irreversible (i.e. probabilistic) computations and provides a reversible let operation (ulet), allowing us to use ancillas (auxiliary qubits) in a modular fashion. QIO programs can be simulated either by calculating a probability distribution or by embedding it into the IO monad using the random number generator. As an example we present a complete implementation of Shor’s algorithm.
Reasoning Formally about Quantum Systems: An Overview
, 2005
"... This article is intended as an introduction to the subject of quantum logic, and as a brief survey of the relevant literature. Also discussed here are logics for speci cation and analysis of quantum information systems, in particular, recent work by P. Mateus and A. Sernadas, and also by R. van der ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This article is intended as an introduction to the subject of quantum logic, and as a brief survey of the relevant literature. Also discussed here are logics for speci cation and analysis of quantum information systems, in particular, recent work by P. Mateus and A. Sernadas, and also by R. van der Meyden and M. Patra. Overall, our objective is to provide a highlevel presentation of the logical aspects of quantum theory. Mateus ' and Sernadas ' EQPL logic is illustrated with a small example, namely the state of an entangled pair of qubits. The "KT" logic of van der Meyden and Patra is demonstrated brie y in the context of the B92 protocol for quantum key distribution. 1
Abstract
, 2005
"... We propose a calculus of local equations over oneway measurement patterns [1], which preserves interpretations, and allows the rewriting of any pattern to a standard form where entanglement is done first, then measurements, then local corrections. We infer from this that patterns with no dependenci ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We propose a calculus of local equations over oneway measurement patterns [1], which preserves interpretations, and allows the rewriting of any pattern to a standard form where entanglement is done first, then measurements, then local corrections. We infer from this that patterns with no dependencies, or using only Pauli measurements, can only realise unitaries belonging to the Clifford group. 1
Quipper: A Scalable Quantum Programming Language
, 1304
"... The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higherorder q ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higherorder quantum programming language. Quipper has been used to program a diverse set of nontrivial quantum algorithms, and can generate quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze quantum algorithms.
Quantum Entanglement Analysis based on Abstract Interpretation
, 801
"... Abstract. Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover, any quantum algorithm which does not create entangl ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover, any quantum algorithm which does not create entanglement can be efficiently simulated on a classical computer. The exact role of the entanglement is nevertheless not well understood. Since an exact analysis of entanglement evolution induces an exponential slowdown, we consider approximative analysis based on the framework of abstract interpretation. In this paper, a concrete quantum semantics based on superoperators is associated with a simple quantum programming language. The representation of entanglement, i.e. the design of the abstract domain is a key issue. A representation of entanglement as a partition of the memory is chosen. An abstract semantics is introduced, and the soundness of the approximation is proven. 1
A system F accounting for scalars
, 2010
"... The algebraic λcalculus [40] and the linearalgebraic λcalculus [3] extend the λcalculus with the possibility of making arbitrary linear combinations of λcalculus terms (preserving ∑ αi.ti). In this paper we provide a finegrained, System Flike type system for the linearalgebraic λcalculus (L ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The algebraic λcalculus [40] and the linearalgebraic λcalculus [3] extend the λcalculus with the possibility of making arbitrary linear combinations of λcalculus terms (preserving ∑ αi.ti). In this paper we provide a finegrained, System Flike type system for the linearalgebraic λcalculus (Lineal). We show that this scalar type system enjoys both the subjectreduction property and the strongnormalisationproperty, which constitute our main technical results. The latter yields a significant simplification of the linearalgebraic λcalculus itself, by removing the need for some restrictions in its reduction rules – and thus leaving it more intuitive. But the more important, original feature of this scalar type system is that it keeps track of ‘the amount of a type’ that this present in each term. As an example, we show how to use this type system in order to guarantee the welldefiniteness of probabilistic functions ( ∑ αi = 1) – thereby specializing Lineal into a probabilistic, higherorder λcalculus. Finally we begin to investigate the logic induced by the scalar type system, and prove a nocloning theorem expressed solely in terms of the possible proof methods in this logic. We discuss the potential connections with Linear Logic and Quantum Computation.
A Hierarchy of Quantum Semantics
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
Abstract
 Add to MetaCart
Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be