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CRC Press eBooks

Quantum Computation

Richard Hughes

Published Nov 15, 2018• 2 citations

Abstract

The remarkable developments in theoretical and experimental quantum computation that have been inspired by Feynman’s seminal papers on the subject are reviewed. Following an introduction to quantum computation, the implications for cryptography of quantum factoring are discussed. The requirements and challenges for practical quantum computational hardware are illustrated with an overview of the ion trap quantum computation project at Los Alamos. The physical limitations to quantum computation with trapped ions are analyzed and an assessment of the computational potential of the technology is made. … it seems that the laws of physics present no barrier to reducing the size of computers until bits are the size of atoms, and quantum behavior holds dominant sway.” R. P. Feynman, 1985 [ 1 ]. “I think I can safely say that nobody understands quantum mechanics.” R. P. Feynman, 1965 [ 2 ].

DOI: 10.1201/9780429500459-14

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Quantum computing represents a transformative paradigm that exploits the principles of quantum mechanics—superposition, entanglement, and quantum interference—to perform computations beyond the capabilities of classical computers. This review presents a comprehensive overview of the fundamental concepts underlying quantum computation, including qubits, quantum gates, quantum algorithms and measurement theory. It further examines major physical implementations of quantum computers, such as superconducting circuits, trapped ions, photonic systems, spin-based qubits, and topological approaches, highlighting their operational principles, advantages, and technological limitations. Key challenges hindering large-scale quantum computation—decoherence, error rates, qubit scalability, and fault tolerance—are critically discussed. Additionally, recent progress in quantum error correction, hybrid quantum–classical algorithms, and hardware optimization is summarized. The review concludes by outlining future research directions and potential applications of quantum computing in cryptography, materials science, optimization, and drug discovery. By integrating theoretical foundations with experimental advancements, this article aims to provide a clear and accessible reference for students, researchers, and scientists entering the rapidly evolving field of quantum computing.