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SIMULATION AND EVALUATE THE PERFORMANCE OF GROVER’S ALGORITHM WITH RESPECT TO CLASSICAL ALGORITHM

Adit Hasan, Jahangir Kabir Atahar Hossain

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

The rapid progress of Computer Science and Engineering has been accompanied by a corresponding evaluation of computation, from classical computation to quantum computation. In classical computation, computer memory made up of bits, where each bit represents either a one or a zero. In quantum computation, there are some quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Instead of using bits, quantum computation uses qubits (quantum bits). A single qubit can represent a one, a zero, or both at the same time, which is called superposition. Because of this ability, quantum computation can perform many tasks simultaneously, faster than classical computing.

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The rapid progress of Computer Science and Engineering has been accompanied by a corresponding evaluation of computation, from classical computation to quantum computation. In classical computation, computer memory made up of bits, where each bit represents either a one or a zero. In quantum computation, there are some quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Instead of using bits, quantum computation uses qubits (quantum bits). A single qubit can represent a one, a zero, or both at the same time, which is called superposition. Because of this ability, quantum computation can perform many tasks simultaneously, faster than classical computing.
Quantum computing represents the leading edge of computational technology, leveraging the principles of quantum mechanics to execute targeted computations much faster than classical computers. In contrast to classical bits, which are limited to representing either 0 or 1, qubits, or quantum bits, exhibit the extraordinary property of superposition. This distinctive characteristic enables qubits to simultaneously occupy multiple states, empowering quantum computers to explore numerous potential solutions to a problem concurrently. This feature makes quantum computing particularly potent for specific tasks. Recent research endeavors have been sparked by the potential of advanced quantum computing technology, leading to the creation of simulations of quantum computers using classical hardware. Grover's quantum search algorithm serves as a notable illustration of quantum computing application, enabling quantum computers to conduct a database search within an unsorted array with a quadratic speedup in time efficiency compared to classical computers. This document presents the quantum Grover search algorithm and its application through 5-qubit quantum circuits, as well as a design framework to simplify the creation of an oracle for a greater number of qubits.
Quantum computing represents one of the most exciting and promising frontiers in computer science and physics. Unlike classical computing, which relies on bits that can exist in one of two states (0 or 1), quantum computing uses qubits (quantum bits) that can exist in superpositions of both simultaneously. This principle, along with other quantum phenomena such as entanglementand quantum interference, allows quantum computers to perform calculations at exponentially faster speeds than classical computers for certain problems. This essay addresses the fundamentals of quantum computing, its applications, current challenges, and its future impact on science and technology, as well as its impact and application in our country.
Quantum computing is a rapidly developing field with the potential to revolutionize our ability to solve certain computational problems . While classical computers operate using classical bits, quantum computers use quantum bits (qubits), which can exist in a superposition of states, allowing for parallel computations. The existence of quantum algorithms, which can solve certain problems exponentially faster than classical algorithms, is one of the most exciting aspects of quantum computing. These exotic algorithms are designed to take advantage of quantum mechanical properties such as entanglement and interference, and have the potential to transform a range of fields, including cryptography, optimization, and machine learning.
The advent of computers has significantly diminished the need for manual computation. As technology has evolved, it has led to the creation of classical computers with high performance, throughput, and memory capacity. Classical computers store data in binary format, using bits that can either be 0 or 1, typically represented by low and high voltage levels, respectively. While effective, this method sometimes demands considerable resources for certain computations. In contrast, quantum computers represent the cutting edge of computing technology. They utilize quantum bits or qubits, which exploit quantum mechanical phenomena like superposition and entanglement, allowing for more efficient problem-solving. This paper presents a simplified overview of the core concepts of quantum computing.
Quantum computing is a rapidly developing field with the potential to revolutionize our ability to solve certain computational problems . While classical computers operate using classical bits, quantum computers use quantum bits (qubits), which can exist in a superposition of states, allowing for parallel computations. The existence of quantum algorithms, which can solve certain problems exponentially faster than classical algorithms, is one of the most exciting aspects of quantum computing. These exotic algorithms are designed to take advantage of quantum mechanical properties such as entanglement and interference, and have the potential to transform a range of fields, including cryptography, optimization, and machine learning.
Quantum computation offers the potential for solving specific problems exponentially faster than the best classical machines, by virtue of its non-classical dynamics and information representation. Quantum mechanical bits (called 'qubits') can be both 0 and 1 at the same time, in which case the qubit is said to be in a superposition state. A quantum gate with input 0 or 1 gives the same output as a classical gate, but if the input is 0 and 1 simultaneously, the quantum gate performs the two corresponding operations simultaneously. Similarly, a 2-qubit gate with an input state prepared as a superposition of the 4 combinations 00, 01, 10 and 11, performs four simultaneous computations. In general, an N-qubit gate could perform 2/sup N/ computations at the same time. So as we increase the size of the system, the computational capacity of the apparatus goes up exponentially, compared to linearly for a classical computer. Using commercial NMR-spectrometers, simple quantum circuits are experimentally implemented consisting of multiple cascaded logic gates.