After publishing my book "Quantum Computing Architecture and Hardware for Engineers: Step by Step" [1] (now I call it Volume I), in which spin qubit and superconducting qubit quantum computers were covered, I decided to continue to write the second volume to cover the trapped ion qubit quantum computer, which was also taught in my EE274 class. I follow the same structure as in Volume I by discussing the physics, mathematics, and their connection to laser pulses and electronics based on how they fulfill the five DiVincenzo's criteria. I also think it would be a good idea to share the second volume on arXiv so that more people can read it for free, and I can continue to update the contents. As of July 2025, I have finished the trapped ion quantum computer part. In the future, I plan to write more critical topics in a step-by-step manner to bridge engineers who did not receive rigorous training in Physics to the quantum computing world.
After publishing my book "Quantum Computing Architecture and Hardware for Engineers: Step by Step" [1] (now I call it Volume I), in which spin qubit and superconducting qubit quantum computers were covered, I decided to continue to write the second volume to cover the trapped ion qubit quantum computer, which was also taught in my EE274 class. I follow the same structure as in Volume I by discussing the physics, mathematics, and their connection to laser pulses and electronics based on how they fulfill the five DiVincenzo's criteria. I also think it would be a good idea to share the second volume on arXiv so that more people can read it for free, and I can continue to update the contents. As of July 2025, I have finished the trapped ion quantum computer part. In the future, I plan to write more critical topics in a step-by-step manner to bridge engineers who did not receive rigorous training in Physics to the quantum computing world.
Quantum Computing Frontiers is a comprehensive academic and professional reference that advances the study of quantum computing from fundamental principles to algorithms, secure communication, error correction, quantum hardware, and emerging technological applications. The book provides an in-depth treatment of quantum gates and circuits, reversible computation, universal gate sets, circuit design and optimization, quantum simulation, measurement-based computing, and adiabatic quantum computing. It explores major quantum algorithms including Deutsch, Deutsch–Jozsa, Bernstein–Vazirani, Simon’s, Grover’s, and Shor’s algorithms, along with amplitude amplification, the Quantum Fourier Transform, and Quantum Phase Estimation. The volume further examines quantum communication and cryptography, including BB84 and E91 quantum key distribution, quantum teleportation, superdense coding, quantum random number generation, post-quantum cryptography, quantum networks, repeaters, security analysis, and the development of a quantum internet. Extensive coverage is given to quantum error correction and fault tolerance, including noise models, decoherence, Shor and Steane codes, stabilizer formalism, fault-tolerant computation, threshold theorems, surface and topological codes, and scalable error-correction architectures. The book also addresses quantum hardware platforms such as superconducting qubits, trapped ions, photonic systems, and spin-based qubits, together with quantum control, measurement, DiVincenzo criteria, quantum annealing, topological quantum computing, quantum simulation, quantum chemistry, hybrid quantum-classical systems, NISQ devices, and applications in optimization, machine learning, and drug discovery. Designed for students, researchers, educators, engineers, and professionals, this volume provides a structured foundation for understanding advanced quantum computing concepts, computational models, quantum security, fault-tolerant architectures, and future directions in quantum technology.
'Quantum Engineering' covers the theory, design, fabrication and applications of quantum coherent solid-state structures. This updated and expanded second edition provides a self-contained presentation of the theoretical methods and experimental results in both first and second waves of quantum technology innovation. Topics span the quantum theory of electric circuits, theoretical methods of quantum optics in application to solid-state circuits, the quantum theory of noise, decoherence and measurements, Landauer formalism for quantum transport, the physics of weak superconductivity and the physics of two-dimensional electron gas in semiconductor heterostructures. The author introduces microscopic ion- and defect-based qubits, currently among the most successful platforms for quantum computation and quantum sensing. Reflecting the significant progress of quantum hardware, state-of-the-art implementations such as quantum metamaterials and quantum reservoir computing are also added to the discussion. Written for graduate students in physics, this book also serves electronic engineers working in quantum engineering.
This is the second paper in a series of papers providing an overview of different quantum computing hardware platforms from an industrial end-user perspective. It follows our first paper on neutral-atom quantum computing. In the present paper, we provide a survey on the current state-of-the-art in trapped-ion quantum computing, taking up again the perspective of an industrial end-user. To this end, our paper covers, on the one hand, a comprehensive introduction to the physical foundations and mechanisms that play an important role in operating a trapped-ion quantum computer. On the other hand, we provide an overview of the key performance metrics that best describe and characterise such a device's current computing capability. These metrics encompass performance indicators such as qubit numbers, gate times and errors, native gate sets, qubit stability and scalability as well as considerations regarding the general qubit types and trap architectures. In order to ensure that these metrics reflect the current state of trapped-ion quantum computing as accurate as possible, they have been obtained by both an extensive review of recent literature and, more importantly, from discussions with various quantum hardware vendors in the field. We combine these factors and provide - again from an industrial end-user perspective - an overview of what is currently possible with trapped-ion quantum computers, which algorithms and problems are especially suitable for this platform, what are the relevant end-to-end wall clock times for calculations, and what might be possible with future fault-tolerant trapped-ion quantum computers.
Unlock the future of quantum technology with this comprehensive guide that bridges the gap between complex quantum theory and real-world applications, giving you the practical edge needed to solve the next generation’s toughest scientific and industrial problems. At its core, quantum computing leverages the principles of quantum mechanics to process information in fundamentally different ways from classical computing. As physical limits constrain the continued scaling of classical technologies, quantum computing offers a fundamentally new pathway toward solving complex problems in science, engineering, and industry. This book is a comprehensive guide designed to bridge the gap between theoretical principles and real-world quantum computing applications. It explores quantum information theory, a cornerstone of quantum computing, to explain how information is encoded, manipulated, and measured in a quantum system. Topics such as quantum gates, circuits, and the Bloch sphere representation are covered in detail, offering readers a solid grounding in the mechanics of quantum operations. With a focus on practical implementation, this book is tailored for students, researchers, and professionals seeking to delve into the transformative world of quantum computing, where the boundaries of classical computation are redefined. Readers will find the book: Uses step-by-step guides and hands-on tutorials for building quantum circuits and running algorithms; Explores core algorithms through detailed walkthroughs of quantum algorithms, including Shor’s, Grover’s, and Quantum Fourier Transform; Provides hands-on learning through exercises, coding challenges, and projects to reinforce practical skills. Audience Academics, researchers, quantum software developers and hardware engineers, data scientists, AI specialists, and security experts focused on the study and implementation of quantum systems and processors.
The superconducting qubit quantum computer is one of the most promising quantum computing architectures for large-scale integration due to its maturity and close proximity to the well-established semiconductor manufacturing infrastructure. From an education perspective, it also bridges classical microwave electronics and quantum electrodynamics. In this paper, we will review the basics of quantum computers, superconductivity, and Josephson junctions. We then introduce important technologies and concepts related to DiVincenzo's criteria, which are the necessary conditions for the superconducting qubits to work as a useful quantum computer. Firstly, we will discuss various types of superconducting qubits formed with Josephson junctions, from which we will understand the trade-off across multiple design parameters, including their noise immunity. Secondly, we will discuss different schemes to achieve entanglement gate operations, which are a major bottleneck in achieving more efficient fault-tolerant quantum computing. Thirdly, we will review readout engineering, including the implementations of the Purcell filters and quantum-limited amplifiers. Finally, we will discuss the nature and review the studies of two-level system defects, which are currently the limiting factor of qubit coherence time. DiVincenzo's criteria are only the necessary conditions for a technology to be eligible for quantum computing. To have a useful quantum computer, large-scale integration is required. We will review proposals and developments for the large-scale integration of superconducting qubit devices. By comparing with the application of electronic design automation (EDA) in semiconductors, we will also review the use of EDA in superconducting qubit quantum computer design, which is necessary for its large-scale integration.
Any new textbook in quantum information has some pretty strong competition to contend with. Not only is there the classic text by Nielsen and Chuang from 2000 [1], but also John Preskill's lecture notes, available for free online [2]. Nevertheless, a proper textbook seems more enduring than online notes, and the field has progressed considerably in the seven years since Nielsen and Chuang was published. A new textbook is a great opportunity to give a snapshot of our current state of knowledge in quantum information. Therein also lies a problem: The field has expanded so much that it is impossible to cover everything at the undergraduate level. Quantum information theory is relevant to an extremely large portion of physics, from solid state and condensed matter physics to particle physics. Every discipline that has some relation to quantum mechanics is affected by our understanding of quantum information theory. Those who wish to write a book on quantum information therefore have to make some profound choices: Do you keep the ultimate aim of a quantum computer in mind, or do you focus on quantum communication and precision measurements as well? Do you describe how to build a quantum computer with all possible physical systems or do you present only the underlying principles? Do you include only the tried and tested ideas, or will you also explore more speculative directions? You don't have to take a black-or-white stance on these questions, but how you approach them will profoundly determine the character of your book. The authors of `Principles of Quantum Computation and Information (Volume II: Basic Tools and Special Topics)' have chosen to focus on the construction of quantum computers, but restrict themselves mainly to general techniques. Only in the last chapter do they explicitly address the issues that arise in the different implementations. The book is the second volume in a series, and consists of four chapters (labelled 5 to 8) called 'Quantum Information Theory', 'Decoherence', 'Quantum Error Correction', and 'First Experimental Implementations'. The first volume covers the basics of classical computation, quantum mechanics, quantum computation, and quantum communication. Chapter five starts with the density matrix formalism, and proceeds with the development of the Kraus representation, POVMs, von Neuman entropy, quantum data compression, the Holevo bound, the partial transpose criterion, and it ends with a very nice section on the various entropies that play a role in modern physics. This includes not only the thermodynamical and statistical entropy, but also the dynamical Kolmogorov–Sinai entropy, which is used in quantum chaos in chapter 6. On the whole, I think that this is a really clear and well-presented chapter. A minor drawback is that the concept of CP maps is not explained as well as it could have been, for example by relating it to the partial transpose criterion. Chapter six continues with the high standard set in chapter five, and presents a very thorough exposition of decoherence in general. It introduces the different decoherence channels, and gives truly excellent explanations of the master equation (tied in with the Kraus representation), quantum jumps, and the quantum trajectory formalism. It also has an elegant explanation for the sensitivity of Schroedinger cats to decoherence. I do miss a proper section on the fidelity of a quantum state, though. The chapter ends with two sections on quantum chaos. Since the authors are experts in this fascinating area, this is a welcome addition to the canon of topics typically covered in quantum information. Unfortunately, the section is quite hard to follow, and as a result it is a bit of a missed opportunity. There is a section on chaos in the first volume of this series, and this may provide the required background. However, for readers who posess only volume II this is of little use. Chapter seven on quantum error correction is disappointing, and I have the feeling that the authors went through the motions without a real passion for the subject matter. The chapter describes various error correction codes, including Hamming codes and CSS codes, but it is virtually silent on fault tolerance; it does not give examples of universal sets of fault tolerant gates, and it does not mention the Solovay–Kitaev theorem. Also, it does not present the stabilizer formalism. All of these are serious omissions in a textbook on quantum information theory. Chapter eight gives a rough sketch of the early simulations and implementations of quantum gates. The readers of this journal will have no trouble following this chapter, but the undergraduate in computer science or mathematics will be completely lost. Most (but not all) physics terms do get a brief explanation, but I doubt whether that is enough to keep non-physicists on board. The chapter covers NMR, cavity QED, ion traps, solid state qubits, and optical implementations of quantum communication. I would have liked to see a more bold choice for the topics covered in the last chapter. For example, whereas liquid-state NMR was an important step in the development of quantum technologies, and many current techniques were invented for it, it does no longer play a role in the design of quantum computers. It would have been better to introduce these techniques in a section on condensed matter systems. Also, as a snapshot of our current state of knowledge in quantum information, I really miss extensive sections on the one-way model of quantum computing [3] and topological quantum computing [4]. In conclusion, the second volume of 'Principles of Quantum Computation and Information' is a partial success. The first two chapters are very good, and I would happily pay £22 for these two chapters alone. However, for a text on quantum error correction the reader is better off with Nielsen and Chuang or Preskill's lecture notes. If the reader wants an overview of quantum information in specific physical systems, there are a host of review articles to choose from, which give more details and are generally more accessible. References [1]M A Nielsen and I L Chuang 2000 Quantum Computation and Quantum Information (Cambridge University Press) [2] J Preskill, http://www.theory.caltech.edu/~preskill/ph229/ [3] R Raussendorf and H J Briegel 2001 A One-Way Quantum Computer Phys. Rev. Lett. 86 5188 [4] A Yu Kitaev 2003 Fault-tolerant quantum computation by anyons Ann. Phys. 303 2