Quantum Algorithms and Applications: Editorial Reviews

A carefully structured guide to the core ideas of quantum algorithms, connecting foundational primitives to real application domains and helping readers build lasting intuition for quantum computational design.

This is an excellent resource for a student or professional coming from a classical STEM background. It manages to be technically rigorous without being impenetrable. If you find standard texts like Nielsen & Chuang too dense for a first pass, this Scaffolding Approach provides the necessary rungs to climb that ladder of complexity.

The one-stop resource for everything quantum computing. Whether you are developing new algorithms or exploring practical applications, this book has it all. True to the clear, signature style of the author’s earlier titles, this latest installment brings complex concepts into sharp focus through masterful presentation.

The field of quantum algorithms is advancing at a very rapid pace, and it is not easy to learn enough to reach the current research frontier. However, with this textbook, readers can efficiently study a wide range of topics, from the fundamentals to state-of-the-art algorithms. I would recommend it as an excellent first introduction for anyone who wishes to pursue research in this field.

Professor Peter Y. Lee and his coauthors, who have been building the Quantum Information Science series through a carefully scaffolded approach, have now published the long-awaited third volume, Quantum Algorithms and Applications, following Quantum Computing and Information (Vol. 1) and Mathematical Foundations of Quantum Computing (Vol. 2). I have used the first volume in teaching quantum information science to a broad range of undergraduate students and have seen an overwhelmingly positive response. This new volume is exceptionally well designed, enabling students to acquire a broad and up-to-date understanding of quantum algorithms and their applications in a clear, systematic, and accessible manner. I expect that many future quantum computer programmers will learn the foundations of using quantum computers from this book.

This book begins with a review of the fundamental concepts of quantum algorithms, followed by detailed explanations of key techniques such as the Quantum Fourier Transform (QFT) and Quantum Phase Estimation (QPE). It then bridges these foundations to Shor’s factoring algorithm. After demonstrating Shor’s algorithm through concrete examples, the discussion expands into the more general framework of Hidden Subgroup Problems.

The book also highlights the importance of Hamiltonian simulation, explaining time evolution as governed by the Schrödinger equation. And variational algorithms based on ansatz are treated with a rigor and depth that is particularly commendable.

Unlike many CS-oriented books, this book devotes substantial space to simulations in physics and chemistry. The Hamiltonian introduced earlier plays a central role here as well. In doing so, the book provides a concrete and efficient approach to simulating nature, staying true to the vision originally envisioned by Feynman.

In addition, readers can explore modern applications such as quantum optimization and quantum machine learning. Together with the other two volumes in the Scaffolding series, this book is likely to become a definitive reference in quantum computing for researchers, engineers, and students alike.

I recently had the opportunity to review the manuscript Quantum Algorithms and Applications: A Scaffolding Approach by Peter Y. Lee, Ran Cheng, and Huiwen Ji.

At more than 600 pages, the manuscript represents a substantial and technically serious contribution to the growing literature on quantum computing. What makes this work stand out is its architectural clarity. Rather than presenting quantum algorithms as isolated results, the book uses a scaffolding methodology that systematically builds the reader’s understanding from foundational principles to modern algorithmic frameworks.

The early chapters establish the conceptual groundwork of quantum computation and computational complexity before moving into the algorithmic core of the field. Topics such as block-encoding techniques, spectral transformations, and quantum linear system algorithms are presented within a structured framework that connects theory to emerging computational use cases.

Equally important is the manuscript’s balanced perspective on the current state of quantum computing. The text recognizes the genuine engineering challenges facing the field today, including noise, qubit scalability, error correction overhead, and the verification of quantum computations. In a field often surrounded by speculation, that level of realism is both refreshing and necessary.

The application discussions are particularly compelling. Examples involving optimization, financial modeling, and infrastructure systems illustrate how quantum algorithmic primitives could eventually intersect with economically and strategically important problems.

Quantum computing remains one of the most intellectually ambitious frontiers in modern science and engineering. Its long-term impact will depend on the co-evolution of hardware scalability, fault-tolerant architectures, and algorithm design. Contributions that strengthen the algorithmic foundation of the field are therefore essential.