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Industrial engineering and management.

How Much Is the Cost of Implementing Arithmetic on a Quantum Computer?

Filippo Giovanni Ghiglieno, Paulo Henrique Dias Ferreira, Vinicius Tribuzi, Olavo Leopoldino da Silva Filho

Published May 29, 2024• 0 citations
Publisher

Abstract

This book chapter explores the transition from classical to quantum computing, emphasizing the capabilities and challenges associated with quantum bits (qubits). Unlike classical computing, where the information is represented as binary digits, known as bits, quantum bits, or qubits, although they share similarities with classical bits, such as 0 and 1 states, they operate in superposition, simultaneously encompassing both 0 and 1 states. This unique property allows quantum computers to perform certain computations, traditionally done sequentially on classical computers, more efficiently, in a single operation with a qubit. Through comparative analysis, we investigate the feasibility and costs of integrating quantum computing into daily applications, examining the potential for personal quantum computing devices. Our findings highlight significant advancements in computational speed of routine mathematical operations, although not yet economically viable or competitive in the current market. Future directions question the market readiness for quantum computing, suggesting a pivotal shift towards cloud-based quantum computing resources.

DOI
10.5772/intechopen.115048

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This book chapter explores the transition from classical to quantum computing, emphasizing the capabilities and challenges associated with quantum bits (qubits). Unlike classical computing, where the information is represented as binary digits, known as bits, quantum bits, or qubits, although they share similarities with classical bits, such as 0 and 1 states, they operate in superposition, simultaneously encompassing both 0 and 1 states. This unique property allows quantum computers to perform certain computations, traditionally done sequentially on classical computers, more efficiently, in a single operation with a qubit. Through comparative analysis, we investigate the feasibility and costs of integrating quantum computing into daily applications, examining the potential for personal quantum computing devices. Our findings highlight significant advancements in computational speed of routine mathematical operations, although not yet economically viable or competitive in the current market. Future directions question the market readiness for quantum computing, suggesting a pivotal shift towards cloud-based quantum computing resources.
ABSTRACT Quantum computing represents a fundamental shift in the way computational problems are approached and solved. Unlike classical computing systems that rely on binary bits to process information, quantum computing utilizes quantum bits, or qubits, which exploit principles of quantum mechanics such as superposition and entanglement. This transition from classical bits to qubits has opened new possibilities for solving complex problems that are computationally infeasible for traditional systems. This paper explores the evolution of computing paradigms from classical architectures to quantum-based models, highlighting the theoretical foundations and technological advancements that have driven this transformation. It discusses the core concepts of quantum computing, including qubit representation, quantum gates, and computational models, along with an overview of current quantum hardware architectures. Furthermore, the paper examines key application areas such as cryptography, optimization, artificial intelligence, and scientific simulations, where quantum computing demonstrates significant potential. Despite its promise, quantum computing faces substantial challenges related to hardware stability, error correction, scalability, and resource requirements, which are also analyzed. Finally, the paper outlines future research directions and the potential impact of quantum computing on next-generation information processing systems, emphasizing its role in redefining the boundaries of modern computation. Keywords : Quantum Computing, Qubits, Quantum Algorithms, Quantum Applications, Future Computing Technologies
Quantum computing is an emerging form of computing that uses the rules of quantum physics to process information in ways that are far different from how computers do it now. Quantum computing uses quantum bits, or qubits, which can exist in superpositions of states and get entangled with each other, which is different from classical computing, which uses a bit that represents binary values (0 or 1). These characteristics allow quantum devices to execute parallel computations, enabling significant speedups for specific categories of problems considered intractable for classical machines. This chapter gives a thorough introduction to quantum computing, starting with a historical overview of its foundations in quantum physics and significant theoretical advancements. It analyzes fundamental ideas including superposition, entanglement, quantum interference, and the no-cloning theorem, explaining how these elements distinguish quantum computation from traditional approaches. The advancement of quantum hardware is examined through several architectures, trapped ions, superconducting circuits, photonics, and topological qubits, together with software frameworks like Qiskit, Cirq, and PennyLane, which support algorithm development and simulation. The chapter examines fundamental quantum algorithms, such as Grover’s algorithm for database search, Shor’s algorithm for integer factorization, and hybrid variational methods designed for noisy intermediate-scale quantum devices. The practical applications in domains including as encryption, optimization, machine learning, chemistry, and finance emphasize the real-world significance of quantum technology. Challenges like decoherence, noise, scalability, and algorithmic maturity are rigorously analyzed, followed by an anticipated discourse on future trajectories including fault-tolerant architectures, quantum networking, and the development of quantum cloud services. This chapter presents a fundamental introduction for students, researchers, and practitioners seeking to comprehend the essential principles, functionalities, and possibilities of quantum computing in the post–Moore’s law period.
Abstract: Quantum computing, an interdisciplinary field blending quantum mechanics and computer science, holds promise to revolutionize computational capabilities. Unlike classical computers, which utilize bits to process information in a binary fashion, quantum computers deploy qubits, capable of existing in multiple states simultaneously due to superposition. This unique property, paired with entanglement, offers unparalleled processing power, positioning quantum computing to tackle problems deemed unsolvable by classical means. While heralded for potential applications in cryptography, drug discovery, and complex modeling, quantum computing faces challenges including decoherence, scalability, and error correction. This paper delves into the foundational principles of quantum computing, its current advancements, the vast applications it could revolutionize, and the significant challenges and societal implications it brings. Through comprehensive exploration, we aim to shed light on both the transformative potential of quantum computing and the hurdles that lay in its path.
Quantum computing represents a monumental leap in computational technology, leveraging the principles of quantum mechanics to solve complex problems at unprecedented speeds. Unlike classical computers, which rely on bits as the smallest unit of information, quantum computers utilize qubits that can exist in multiple states simultaneously, enabling them to perform many calculations at once. This paper delves into the foundational concepts of quantum computing, including superposition, entanglement, and quantum gates, and explores its potential applications across various domains, such as cryptography, drug discovery, optimization problems, and artificial intelligence. We will discuss current advancements in quantum technology, high-lighting key breakthroughs and the progress made by leading research institutions and companies. Furthermore, this paper addresses the significant challenges that quantum computing faces, including error rates, qubit coherence, and scalability, which hinder its widespread adoption. By examining these facets, we aim to provide a comprehensive overview of how quantum computing could transform various fields and the hurdles that must be overcome to realize its full potential, ultimately suggesting future directions for research and development in this revolutionary area of technology.
Quantum computing represents a transformative shift in computational paradigms, offering unprecedented potential for solving complex problems beyond the reach of classical computers. This paper explores the theoretical foundations of quantum computing, including quantum bits (qubits), superposition, entanglement, and quantum gates, and examines their implications for computation. Utilizing a qualitative approach, this study conducts a comprehensive literature review and library research to analyze the current state of quantum computing technology, its applications, and the challenges it faces in practical implementation. The findings reveal significant advancements in quantum algorithms, such as Shor's and Grover's algorithms, which demonstrate the capability of quantum computing to revolutionize fields like cryptography, optimization, and materials science. However, the research also highlights the technical challenges, including qubit stability, error correction, and scalability, which must be addressed to transition from theoretical models to practical applications. Additionally, the study discusses the ethical and societal implications of quantum computing, particularly in relation to data security and privacy. The paper concludes by outlining future research directions and potential real-world applications, emphasizing the need for interdisciplinary collaboration to fully realize the potential of quantum computing in solving some of the most pressing global challenges.
Quantum computing represents a paradigm shift in computational technology, promising to revolutionize the way we approach complex problems across various domains. Unlike classical computing, which relies on bits as the smallest unit of information, quantum computing leverages quantum bits or qubits, which can exist in multiple states simultaneously due to the principles of superposition and entanglement. This article delves into the potential of quantum computing to address real-world complex problems, exploring its theoretical foundations, current advancements, and future prospects. We examine key areas where quantum computing could have a transformative impact, including cryptography, optimization, drug discovery, artificial intelligence, and climate modeling. Additionally, we present three detailed tables summarizing the comparative advantages of quantum computing over classical methods, the current state of quantum hardware, and the potential applications of quantum algorithms. The article concludes with a discussion on the challenges and ethical considerations associated with the widespread adoption of quantum computing.