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d CARTESIAN

Derivation of Quantum Guarded Command Language Program for Average

Cherry Telap, Benny Pinontoan, Jullia Titaley

Published Jun 26, 2015• 0 citations
Publisher

Abstract

Has conducted research to determine the derivation of quantum guarded command language (qGCL) program for average. Initially calculation of average value was made in guaded command language (GCL) which is then implemented on a digital computer into the Pascal programming language. Furthermore GCL to calculate the average value was analyzed again to be made in the quantum guarded command language (qGCL). qGCL implementation is on a quantum computer is a future computer could perform calculations very quickly because it uses a superposition state is referred to as quantum bits (qubits). Keywords : GCL, qGCL, Quantum Computer

DOI
10.35799/dc.4.2.2015.9055

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Has conducted research to determine the derivation of quantum guarded command language (qGCL) program for average. Initially calculation of average value was made in guaded command language (GCL) which is then implemented on a digital computer into the Pascal programming language. Furthermore GCL to calculate the average value was analyzed again to be made in the quantum guarded command language (qGCL). qGCL implementation is on a quantum computer is a future computer could perform calculations very quickly because it uses a superposition state is referred to as quantum bits (qubits). Keywords : GCL, qGCL, Quantum Computer
On a classical computer or a binary computer, calculations are done simultaneously so as to produce the equations and algorithms. The result of this research shows that to determined maximum value specified in the algorithm using quantum Guarded-Command Language (qGCl) in quantum computer. Initially determine of maximum value was construct in Djikstra’s Guarded-Command Language (GCL) which is then implemented on Zuliani’s probability Guarded-Command Language (pGCL) furthermore applying to quantum Guarded-Command Language (qGCL) for last result. Of concern here is the speed in resolving a problem or calculate problem. Due to the Quantum Computer has a Quantum Bit (qubit) and a phenomenon commonly called superposition. Keywords: GCL, pGCL, qGCL, quantum computer.
We extract a novel quantum programming paradigm - superposition of programs - from the design idea of a popular class of quantum algorithms, namely quantum walk-based algorithms. The generality of this paradigm is guaranteed by the universality of quantum walks as a computational model. A new quantum programming language QGCL is then proposed to support the paradigm of superposition of programs. This language can be seen as a quantum extension of Dijkstra's GCL (Guarded Command Language). Surprisingly, alternation in GCL splits into two different notions in the quantum setting: classical alternation (of quantum programs) and quantum alternation, with the latter being introduced in QGCL for the first time. Quantum alternation is the key program construct for realizing the paradigm of superposition of programs. The denotational semantics of QGCL are defined by introducing a new mathematical tool called the guarded composition of operator-valued functions. Then the weakest precondition semantics of QGCL can straightforwardly derived. Another very useful program construct in realizing the quantum programming paradigm of superposition of programs, called quantum choice, can be easily defined in terms of quantum alternation. The relation between quantum choices and probabilistic choices is clarified through defining the notion of local variables. We derive a family of algebraic laws for QGCL programs that can be used in program verification, transformations and compilation. The expressive power of QGCL is illustrated by several examples where various variants and generalizations of quantum walks are conveniently expressed using quantum alternation and quantum choice. We believe that quantum programming with quantum alternation and choice will play an important role in further exploiting the power of quantum computing.
In this paper a programming language, qGCL, is presented for the expression of quantum algorithms. It contains the features required to program a 'universal' quantum computer (including initialisation and observation), has a formal semantics and body of laws, and provides a refinement calculus supporting the verification and derivation of programs against their specifications. A representative selection of quantum algorithms are expressed in the language and one of them is derived from its specification.
A method has been developed for transforming a program written in the probabilistic guarded-command language (pGCL) into an equivalent but reversible program. The method extends previous work on logical reversibility to that language and pertains to “demonic” nondeterminism and probability. Use is made of a formal definition of logical reversibility and the expectation-transformer semantics for pGCL. The method should be useful in the compilation of a general-purpose programming language for quantum computation.
Despite many common concepts with classical computer science, quantum computing is still widely considered as a special discipline within the broad field of theoretical physics. One reason for the slow adoption of QC by the computer science community is the confusing variety of formalisms (Dirac notation, matrices, gates, operators, etc.), none of which has any similarity with classical programming languages, as well as the rather “physical” terminology in most of the available literature. QCL (Quantum Computation Language) tries to fill this gap: QCL is a hight level, architecture independent programming language for quantum computers, with a syntax derived from classical procedural languages like C or Pascal. This allows for the complete implementation and simulation of quantum algorithms (including classical components) in one consistent formalism. Chapter 1 is an introduction into the basic concepts of quantum programming,
In standard computation, non-determinism is used for specifying programs’ behaviour, without having to specify details of implementation. In quantum computation, non-determinism is either meant to be “classical” probabilism or it is not considered at all, since quantum computation is the physical theory of computation and thus it does not deal with non-implementable features. In this work we will instead show that non-determinism may be useful also in quantum computation. In particular, we consider non-determinism embedded in a programming language for quantum computation, the quantum Guarded-Command Language (qGCL), and use that for describing and reasoning about counterfactual computation and mixed-state systems.