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arXiv:0705.3333

Simulation of Quantum Algorithms with a Symbolic Programming Language

Peter Nyman

Published May 23, 2007• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0705.3333

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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.
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.
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations of some error correction codes. These implementations will be made in a more general quantum simulation language on a classical computer in the language Mathematica. The intention of this research is to develop a programming language that is able to make simulations of all quantum algorithms and error corrections in the same framework. The program code implemented on a classical computer will provide a connection between the mathematical formulation of quantum mechanics and computational methods. This gives us a clear uncomplicated language for the implementations of algorithms.
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations of some error correction codes. These implementations will be made in a more general quantum simulation language on a classical computer in the language Mathematica. The intention of this research is to develop a programming language that is able to make simulations of all quantum algorithms and error corrections in the same framework. The program code implemented on a classical computer will provide a connection between the mathematical formulation of quantum mechanics and computational methods. This gives us a clear uncomplicated language for the implementations of algorithms.
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.
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics and nanotechnology. Understanding and simulating quantum operations on a classical computer has different approaches and is modeled in different ways. However, the most repute ways are Quantum Turing Machine, Network Model or circuit model of connected gates and Quantum Programming Language. Many simulators do exist that varies in many features such as implementation languages, target platforms, paradigms, visuality, and applied quantum algorithms. There was a developmental trade-off between the simplicity and the functionality of the simulator. The goals and research activities are outlined as follows: First, surveying the quantum computing world, its characteristics, issues, problems, and challenges. Second, surveying the existing quantum simulators, illustrating representative simulators of major approaches, their features, and functionalities. Third, introducing a framework to provide the power of quantum computing , while insisting the simplicity and high usability. Finally, providing a case study for a new quantum algorithm based on the introduced framework.