Results 11  20
of
33
1 Quantum Lambda Calculus
"... We discuss the design of a typed lambda calculus for quantum computation. After a brief discussion of the role of higherorder functions in quantum information theory, we define the quantum lambda calculus and its operational semantics. Safety invariants, such as the nocloning property, are enforce ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
We discuss the design of a typed lambda calculus for quantum computation. After a brief discussion of the role of higherorder functions in quantum information theory, we define the quantum lambda calculus and its operational semantics. Safety invariants, such as the nocloning property, are enforced by a static type system that is based on intuitionistic linear logic. We also describe a type inference algorithm, and a categorical semantics. 1.1
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
Programming with Quantum Communication
"... Abstract. We present a formal framework for specifying, implementing, and analysing quantum communication protocols. 1 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. We present a formal framework for specifying, implementing, and analysing quantum communication protocols. 1
Programming with a Quantum Stack
, 2007
"... This thesis presents the semantics of quantum stacks and a functional quantum programming language, LQPL. An operational semantics for LQPL based on quantum stacks in the form of a term logic is developed and used as an interpretation of quantum circuits. The operational semantics is then extend ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This thesis presents the semantics of quantum stacks and a functional quantum programming language, LQPL. An operational semantics for LQPL based on quantum stacks in the form of a term logic is developed and used as an interpretation of quantum circuits. The operational semantics is then extended to handle recursion and algebraic datatypes. Recursion and datatypes are not concepts found in quantum circuits, but both are generally required for modern programming languages. The language LQPL is introduced in a discussion and example format. Various example programs using both classical and quantum algorithms are used to illustrate features of the language. Details of the language, including handling of qubits, general data types and classical data are covered. The quantum stack machine is then presented. Supporting data for operation of the machine are introduced and the transitions induced by the machine’s instructions are given.
Simulation of Quantum Algorithms with a Symbolic Programming Language
, 2008
"... This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. The computational language will include formulatio ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. The computational language will include formulations such as quantum state, superposition and quantum operator. 1
Taming NonCompositionality Using New Binders
"... Abstract. We propose an extension of the traditional λcalculus in which terms are used to control an outside computing device (quantum computer, DNA computer...). We introduce two new binders: ν and ρ. In νx.M, x denotes an abstract resource of the outside computing device, whereas in ρx.M, x denot ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We propose an extension of the traditional λcalculus in which terms are used to control an outside computing device (quantum computer, DNA computer...). We introduce two new binders: ν and ρ. In νx.M, x denotes an abstract resource of the outside computing device, whereas in ρx.M, x denotes a concrete resource. These two binders have different properties (in terms of αconversion, scope extrusion, convertibility) than the ones of standard λbinder. We illustrate the potential benefits of our approach with a study of a quantum computing language in which these new binders prove meaningful. We introduce a typing system for this quantum computing framework in which linearity is only required for concrete quantum bits offering a greater expressiveness than previous propositions. 1
Orthogonality and Algebraic LambdaCalculus
"... Directly encoding lambdaterms on quantum strings while keeping a quantum interpretation is a hard task. As shown by van Tonder (2004), requiring a unitary reduction forces the lambdaterms in superposition to be mostly equivalent. Following instead (Arrighi and DíazCaro, 2009), we show in this not ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Directly encoding lambdaterms on quantum strings while keeping a quantum interpretation is a hard task. As shown by van Tonder (2004), requiring a unitary reduction forces the lambdaterms in superposition to be mostly equivalent. Following instead (Arrighi and DíazCaro, 2009), we show in this note how one can conceive a lambdacalculus with algebraic features and that admits a general notion of orthogonality among lambdaterms, by providing a compiler of the system into unitary maps. 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.
Implementing Grover’s Algorithm Using Linear Transformations in Haskell
"... In contrast to the usual approach to simulating quantum computing algorithms as a series of operations to be performed on a set of “qubits, ” we have used the Haskell programming language to implement Grover’s fast search algorithm as a composition of functional transformations applied, as a final s ..."
Abstract
 Add to MetaCart
In contrast to the usual approach to simulating quantum computing algorithms as a series of operations to be performed on a set of “qubits, ” we have used the Haskell programming language to implement Grover’s fast search algorithm as a composition of functional transformations applied, as a final step, to a set of qubits (a “quantum register”). In this approach, which has been (at least implicitly) suggested in the literature, but, as far as we have been able to determine, not been realized in a working program, the composition is constructed by means of common matrix manipulations and takes advantage of the associativity of matrix operations to eliminate complicated computations usually associated with simulating quantum computations. We present the crucial code sections, along with actual program results. We discuss the implications of our approach in the areas of quantum program simulation, algorithm analysis, algorithm construction, and construction of languages for quantum programming.
Extending scientific computing system with structural quantum programming capabilities
, 2010
"... Abstract. We present the basic highlevel structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudocode based on QCL quantum programming language to describe them. We also present ..."
Abstract
 Add to MetaCart
Abstract. We present the basic highlevel structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudocode based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantumoctave providing library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate highlevel programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for higllevel quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantumoctave package. This is possible thanks to the ability to operate on density matrices implemented in quantumoctave. Key words: quantum information, quantum programming, models of quantum computation. 1.