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Probabilistic aspects of quantum programming

Jarosław Adam Miszczak

Published Feb 23, 2013• 2 citations
OpenAlex

Abstract

Quantum information theory allows us to use quantum mechanics resources for processing and sending information. Since the rules of quantum mechanics are in many aspects counterintuitive, the development of new quantum algorithms and protocols is complicated. At the moment only a few algorithms exist which can be executed on a quantum computer with significant improvement in speed or memory usage. \n \nThe main goal of this thesis is to describe the methods of using quantum programming languages for developing new quantum algorithms. We present the original implementation of a classical game where quantum programming was used to develop and analyse quantisation of the game. We also show how quantum data types, ie. data types allowing for storing superposition of values, can be used to develop new quantum algorithms.

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Quantum information theory allows us to use quantum mechanics resources for processing and sending information. Since the rules of quantum mechanics are in many aspects counterintuitive, the development of new quantum algorithms and protocols is complicated. At the moment only a few algorithms exist which can be executed on a quantum computer with significant improvement in speed or memory usage. \n \nThe main goal of this thesis is to describe the methods of using quantum programming languages for developing new quantum algorithms. We present the original implementation of a classical game where quantum programming was used to develop and analyse quantisation of the game. We also show how quantum data types, ie. data types allowing for storing superposition of values, can be used to develop new quantum algorithms.
Quantum mechanics and game theory were developed at almost the same time, during the first half of 20th century.Classical game theory is one of the most developed in mathematics and computer science.It has many applications in economics, biology, and different kinds of social science.In computer science, many cryptographic protocols are also based on the elements of game theory.Quantum computing is a relatively new branch of computer science.It unites different aspects of complexity theory and quantum physics.Our intention is to take it one step further and combine classical game theory with the acquired knowledge of quantum computing; in particular, to study the effects of using quantum information in the well-known problems of game theory.In this thesis, we obtain several bounds on the values of some special classes of nonlocal quantum games, and we present a new scheme for games quantization.
A general quantum simulation language on a classical computer provides the opportunity to compare an experiential result from the development of quantum computers with mathematical theory. The intention of this research is to develop a program language that is able to make simulations of all quantum algorithms in same framework. This study examines the simulation of quantum algorithms on a classical computer with a symbolic programming language. We use the language Mathematica to make simulations of well-known quantum algorithms. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. This gives us an uncomplicated and clear language for the implementations of algorithms. The computational language includes essential formulations such as quantum state, superposition and quantum operator. This symbolic programming language provides a universal framework for examining the existing as well as future quantum algorithms. This study contributes with an implementation of a quantum algorithm in a program code where the substance is applicable in other simulations of quantum algorithms.
Quantum Computation is an interdisciplinary field formed by the merge of quantum effect, information theory and algorithms. The future of computing lies with the quantum computers which may be a hypothetical paradigm but surely will be a reality very soon.This book describes about some quantum algorithms and programs which will prove as the foundation of quantum computers in the years to come.In quantum computers we exploit quantum effects to compute in ways that are faster or moreefficient than, or even impossible, on conventional computers. Quantum computers use aspecific physical implementation to gain a computational advantage over conventionalcomputers. Properties called superposition and entanglement may, in some cases, allow anexponential amount of parallelism. Also, special purpose machines like quantumcryptographic devices use entanglement and other peculiarities like quantum uncertainty.Quantum computing combines quantum mechanics, information theory, and aspects ofcomputer science. The field is a relatively new one that promises secure data transfer,dramatic computing speed increases, and may take component miniaturization to itsfundamental limit.
Abstract Programming a quantum computer can be thought of as having two steps. The first has been the subject of the past several chapters: leveraging number theory, superposition, entanglement, gates, and measurements to develop an algorithm to solve a problem. Classically, computer programmers do not work at the level of gates and there is, of course, no such thing in their world as entanglement or superposition. They work at the second level, writing code to implement the algorithm. There are several universal languages available for classical programming. This chapter provides resources for programming quantum computers using these standard languages.
Modern trends in the development of society require the rapid processing of a significant amount of information. Under these conditions, the issue of creating quantum computing devices that are many times greater than the computing capabilities of existing machines is topical. On the way to creating a quantum computer, quantum algorithms are currently being researched. The purpose of this work was to develop a program that allows simulating a quantum algorithm on a classical computer. The C# language was chosen for the implementation of the software implementation. The paper considers various quantum algorithms, explores the possibilities of emulating quantum computing on existing computers by conducting experimental studies.