This chapter explores the evolution of superconducting qubits from traditional superconductors, tracing the scientific and technological milestones that have led to their central role in quantum computing. Beginning with an overview of superconductivity, the Josephson effect, qubits, and their types, the chapter highlights superconducting qubits with their theoretical implementation. It then transitions to the development of modern qubit architectures – charge, flux, and transmon qubits – emphasizing advances in material purity, fabrication, and coherence enhancement. Special focus is given to a short description of fabricating granular aluminum qubits for quantum engineering applications. The chapter concludes with current challenges, including decoherence mitigation, material scalability, and integration with hybrid quantum systems. This work aims to provide readers with a comprehensive understanding of the journey from conventional superconductors to quantum information devices.
This chapter explores the evolution of superconducting qubits from traditional superconductors, tracing the scientific and technological milestones that have led to their central role in quantum computing. Beginning with an overview of superconductivity, the Josephson effect, qubits, and their types, the chapter highlights superconducting qubits with their theoretical implementation. It then transitions to the development of modern qubit architectures – charge, flux, and transmon qubits – emphasizing advances in material purity, fabrication, and coherence enhancement. Special focus is given to a short description of fabricating granular aluminum qubits for quantum engineering applications. The chapter concludes with current challenges, including decoherence mitigation, material scalability, and integration with hybrid quantum systems. This work aims to provide readers with a comprehensive understanding of the journey from conventional superconductors to quantum information devices.
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.
Abstract Superconducting qubits are multilevel micro-fabricated artificial atoms based on superconducting materials. They are mainly operated in the low microwave frequency range (2–8 GHz) and require to be cooled below 20 mK to maintain quantum coherence. They enable precise engineering of transition frequencies and coupling strengths, facilitating advancements in quantum information processing and light-matter interactions. The field has evolved from early devices, characterized by short coherence times, to modern architectures with improved noise resilience, scalability, and fidelity. Better performances have been achieved through innovations in materials, fabrication, control electronics, and circuit design, enabling qubits with millisecond coherence times and gate fidelities exceeding 99.9%. However, challenges remain in mitigating two-level system defects, scaling devices, and addressing the cryogenic and infrastructure needs of larger quantum processing units. Current research focuses on modular and scalable architectures, error correction, and application. The field’s progress highlights the potential for superconducting qubits to drive advancements in quantum computation.
Hybrid semiconductor-superconductor qubits have recently emerged as a promising alternative to traditional platforms, combining material advantages with device-level tunability. A defining feature is their gate-tunable Josephson coupling, enabling superconducting qubit architectures with full electric-field control and offering a path toward scalable, low-crosstalk quantum processors. This approach seeks to merge benefits of superconducting and semiconductor qubits, for instance by encoding quantum information in the spin of a quasiparticle occupying an Andreev bound state, thus combining long coherence times with fast, flexible control. Progress has accelerated through bottom-up engineering of Andreev states in coupled quantum dot arrays, leading to architectures such as minimal Kitaev chains hosting Majorana zero modes. In parallel, Hamiltonian-protected designs aim to enhance resilience against local noise and decoherence by exploiting superconducting phase dynamics and discrete charge or flux degrees of freedom. This article reviews recent theoretical and experimental advances in hybrid qubits, providing an overview of physical mechanisms, device implementations, and emerging architectures, with emphasis on their potential for (topologically) protected quantum information processing. While many designs remain at proof-of-concept stage, rapid progress suggests practical demonstrations may soon be achievable.
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.
Quantum device fabrication and integration represent a critical frontier in the advancement of next-generation computing and communication technologies. This chapter provides an overview of the fundamental principles and processes involved in the fabrication of quantum devices, including superconducting qubits, semiconductor quantum dots, and spin-based devices. Key fabrication techniques such as advanced lithography, thin-film deposition, etching, and material characterization are discussed, with emphasis on the stringent requirements for precision, material purity, and defect control. The chapter also addresses challenges associated with integrating quantum devices with classical CMOS electronics, including cryogenic operation, interconnect design, scalability, and noise mitigation. By examining current fabrication approaches and integration strategies, this chapter highlights the technological barriers and emerging solutions shaping scalable quantum systems. The discussion offers readers a foundational understanding of how quantum devices are realized and integrated, bridging the gap between quantum physics and practical hardware implementation.
As superconducting circuits emerge as a leading platform for scalable quantum information processing, building comprehensive bridges from the foundational principles of macroscopic quantum phenomena to the architecture of modern quantum devices is increasingly essential for introducing new researchers to the field. This tutorial provides a self-contained, pedagogical introduction to superconducting quantum circuits at the undergraduate level. Beginning with an overview of superconductivity and the Josephson effect, the tutorial systematically develops the quantization of microwave circuits into the framework of circuit quantum electrodynamics (cQED). The transmon qubit is then introduced as a state-of-the-art application, with a detailed derivation of its Hamiltonian and its interaction with control and readout circuitry. The theoretical formalism is consolidated through a numerical simulation of vacuum Rabi oscillations in a driven transmon-resonator system, a canonical experiment that demonstrates the coherent energy exchange characteristic of the strong coupling regime. This work serves as a foundational guide and first point of contact, equipping students and researchers with the conceptual and mathematical tools necessary to understand and engineer superconducting quantum hardware.