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Apress eBooks

Theory of Superconducting Qubit

Subhojit Halder, Kinjal A. Chauhan, Muhamad Bagher Barfar, Srinjoy Ganguly, Shalini Devendrababu

Published Jan 1, 2025• 0 citations
Publisher

Abstract

This chapter explores the foundational concepts underlying superconducting qubits, pivotal in modern quantum computing. It begins with the harmonic oscillator, fundamental to both classical and quantum mechanics. Section 2.1 introduces its classical and quantum descriptions, emphasizing energy quantization and assessing its potential as a qubit. Section 2.2 focuses on the quantum LC oscillator, integral to superconducting circuit theory. Starting with the classical dynamics of an LC circuit, we derive its Hamiltonian and transition to its quantum description using ladder operators. This section bridges classical circuit theory and quantum systems, paving the way to understanding superconducting qubits. Sections 2.3–2.5 examine key qubit types. Section 2.3 introduces phase, charge, and flux qubits, highlighting their operational principles and the physical parameters they encode, such as magnetic flux or electric charge. Section 2.4 delves into the transmon qubit, exploring its Hamiltonians and methods for control and measurement. Finally, Section 2.5 surveys recent advancements in superconducting qubit designs, offering insights into the evolution toward next-generation qubits. This chapter provides a comprehensive framework for understanding superconducting qubits, linking classical systems to quantum technologies, and contextualizing their role in advancing quantum computation.

DOI
10.1007/979-8-8688-1504-1_2

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This chapter explores the foundational concepts underlying superconducting qubits, pivotal in modern quantum computing. It begins with the harmonic oscillator, fundamental to both classical and quantum mechanics. Section 2.1 introduces its classical and quantum descriptions, emphasizing energy quantization and assessing its potential as a qubit. Section 2.2 focuses on the quantum LC oscillator, integral to superconducting circuit theory. Starting with the classical dynamics of an LC circuit, we derive its Hamiltonian and transition to its quantum description using ladder operators. This section bridges classical circuit theory and quantum systems, paving the way to understanding superconducting qubits. Sections 2.3–2.5 examine key qubit types. Section 2.3 introduces phase, charge, and flux qubits, highlighting their operational principles and the physical parameters they encode, such as magnetic flux or electric charge. Section 2.4 delves into the transmon qubit, exploring its Hamiltonians and methods for control and measurement. Finally, Section 2.5 surveys recent advancements in superconducting qubit designs, offering insights into the evolution toward next-generation qubits. This chapter provides a comprehensive framework for understanding superconducting qubits, linking classical systems to quantum technologies, and contextualizing their role in advancing quantum computation.
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Build quantum computers using superconducting qubits and microwave cavity technology Creating qubits with sufficiently long coherence times remains one of the central challenges in building practical quantum computers. Quantum Computing with Superconducting Qubits and Cavities unites the latest advances in superconducting qubits, ultra-high-Q microwave cavities, and cavity–transmon architectures that are emerging as one of the leading platforms for scalable, fault-tolerant quantum computing. By combining conceptual insight with practical implementation, the book equips readers to understand not only how these systems work, but why they are at the forefront of the quantum technology revolution. The book explores quantum computation using bosonic modes, Fock states, qudits, quantum memories, and modern bosonic error-correcting codes including cat, binomial, and GKP encodings. Fundamental concepts are developed through clear physical explanations, while rigorous mathematical treatments are introduced where needed to provide a deeper understanding. Dedicated reviews of the underlying principles of quantum physics make the material accessible to newcomers without sacrificing the depth expected by researchers and practicing engineers. Quantum Computing with Superconducting Qubits and Cavities also includes: Design principles and operation of superconducting transmon qubits integrated with high-coherence microwave cavities for scalable quantum architectures. Bosonic quantum error-correction strategies that dramatically extend coherence and move quantum computing closer to fault-tolerant operation. Applications of quantum computing, including integer factoring, database searching, quantum chemistry, condensed-matter physics, and materials science simulations beyond the reach of classical computers. Materials science, fabrication methods, and surface treatments that continue to drive record improvements in qubit and cavity coherence. The global race toward quantum computing, including major international investments and the rapidly expanding role of superconducting quantum technologies. Written for physicists, materials scientists, electrical engineers, computer scientists, graduate students, and researchers entering quantum information science, this book provides both the theoretical foundation and the practical knowledge needed to engage with one of the fastest-growing fields in modern science and engineering.
"Introduction to Quantum Mechanics And Quantum Computing" is a comprehensive book chapter that provides an in-depth exploration of the groundbreaking field of quantum computing. Beginning with an introduction to the fundamental principles of quantum mechanics, the chapter navigates through the evolution of quantum computing, from its conceptual origins to the challenges faced in its development. The core concepts of quantum bits (qubits) and their unique properties, such as entanglement and superposition, are explained, laying the foundation for understanding quantum information processing. The chapter further delves into the building blocks of quantum computing—qubits—detailing their diverse physical implementations. Quantum gates and circuits, analogous to classical computing, are explored, shedding light on the mechanisms enabling quantum algorithms to perform complex tasks efficiently. Highlighting renowned algorithms like Shor's and Grover's, the chapter emphasizes the potential computational supremacy of quantum computers over classical counterparts. Recognizing the sensitivity of quantum systems to noise and decoherence, the chapter introduces quantum error correction as a crucial aspect of ensuring reliable quantum computation. The exploration concludes with an examination of the current state of quantum computing, outlining progress in industry and academia while addressing the challenges in building large-scale, fault-tolerant quantum computers. The potential applications of quantum computing in cryptography, drug discovery, optimization problems, and beyond are discussed, offering a glimpse into the transformative impact this emerging technology may have on various industries. "Introduction to Quantum Mechanics And Quantum Computing" serves as a comprehensive guide for readers seeking a nuanced understanding of the theoretical foundations and practical applications of quantum computing.
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