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The Materials Research Society series

Superconducting Qubits

Ray LaPierre

Published Oct 24, 2025• 0 citations
Publisher

Abstract

Thus far, we have examined quantum computing based on electron states in atoms, ions and semiconductor structures. In this chapter, we will examine quantum states in superconductors and their application as qubits. This chapter is particularly extensive due to the large variety of possible superconducting quantum circuits. We introduce superconductivity and examine the three main types of superconducting qubit: the flux qubit, the charge qubit and the phase qubit. We will also examine the transmon qubit and circuit quantum electrodynamics.

DOI
10.1007/978-3-031-90731-9_22

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Thus far, we have examined quantum computing based on electron states in atoms, ions and semiconductor structures. In this chapter, we will examine quantum states in superconductors and their application as qubits. This chapter is particularly extensive due to the large variety of possible superconducting quantum circuits. We introduce superconductivity and examine the three main types of superconducting qubit: the flux qubit, the charge qubit and the phase qubit. We will also examine the transmon qubit and circuit quantum electrodynamics.
Thus far, we have examined quantum computing based on single particle states in atoms, ions and semiconductor structures. In this chapter, we will examine quantum states in superconductors and their application as qubits. This chapter is particularly extensive due to the large variety of possible superconducting quantum circuits. We introduce superconductivity and examine the three main types of superconducting qubit: the flux qubit, the charge qubit and the phase qubit. We will also examine the transmon qubit and circuit quantum electrodynamics.
Superconducting quantum bits (qubits) and circuits are the leading candidate for the implementation of solid-state quantum computation. They have also been widely used in a variety of studies of quantum physics, atomic physics, quantum optics, and quantum simulation. In this article, we will present an overview of the basic principles of the superconducting qubits, including the phase, flux, charge, and transmon (Xmon) qubits, and the progress achieved so far concerning the improvements of the device design and quantum coherence property. Experimental studies in various research fields using the superconducting qubits and circuits will be briefly reviewed.
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.
We introduce the notion of qubit as unit of quantum information, illustrating how this notion can be implemented in nonlinear superconducting circuits via the charge and current degrees of freedom. Within these two types of qubits, we discuss the charge qubit, the transmon, and the flux qubit, illustrating the nature of the states that implement the qubit subspace and how they can be controlled and measured. We discuss how qubits can interact with each other directly or through mediators, illustrating different limits of interaction, introducing the notion of dipolar electric and magnetic moments, and demonstrating the tunability of interactions by different means. The chapter closes with a brief study of qubit coherence along the history of this field, with an outlook to potential near-term improvements.