After two years of focused preparation and careful editing, we are excited to announce the release of our third book, Quantum Algorithms and Applications: A Scaffolding Approach.
This book presents a progressive scaffolding approach that guides readers from core primitives to practical workflows in simulation, optimization, quantum machine learning, and linear systems, with an emphasis on mastering concepts and principles that transfer across platforms and problem settings.
Features
- A systematic, student-friendly route through quantum algorithms.
- Comprehensive coverage, from core primitives to real applications.
- Up to date: quantum singular value transformation (QSVT), sampling-based quantum diagonalization (SQD), quantum machine learning (QML), classical shadows, differential-equation solvers, and the quest for quantum advantage.
Authors
- Dr. Peter Y. Lee (Ph.D., Princeton University) — quantum nanostructures; teaching and academic program leadership.
- Dr. Ran Cheng (Ph.D., The University of Texas at Austin) — condensed matter theory; award-winning physicist.
- Dr. Huiwen Ji (Ph.D., Princeton University) — quantum chemistry; accomplished researcher and award recipient.
Why this book
We wrote this book to help readers develop concept-first understanding that remains useful as tools and platforms change. In quantum algorithms, details of software stacks evolve quickly, but the underlying primitives, assumptions, and resource tradeoffs are what determine whether a workflow is sound and whether an advantage claim is meaningful. Our goal is to cultivate the ability to translate a problem statement into a quantum workflow, identify the dominant costs, and reason clearly about what is feasible on near-term devices and what becomes compelling as fault tolerance matures.
Parts of the Book
This book is organized into four parts.
Part I: Foundations of Quantum Algorithms.
We establish the computational viewpoint used throughout the book, including algorithmic efficiency, the circuit and query models, and the complexity language needed to reason about scaling, precision, and success probability.
Part II: Core Quantum Algorithms.
We develop the core algorithmic primitives that reappear across quantum speedups: Fourier-based methods (quantum Fourier transform and quantum phase estimation), period finding and Shor’s algorithm, amplitude amplification and estimation, and modern polynomial-approximation frameworks centered on block encodings, including linear combination of unitaries, quantum signal processing, and quantum singular value transformation.
Part III: Quantum Simulation in Physics and Chemistry.
We show how the toolkit is used for simulation tasks motivated by physics and chemistry. The emphasis is on how physical structure becomes computational structure through Hamiltonians, encodings, and measurement strategies, and on how accuracy, cost, and feasibility trade off in practice.
Part IV: Other Applications.
We survey additional areas where the same primitives recur, including optimization, quantum machine learning, and quantum methods for linear systems and differential equations, with attention to input/output models, verification, and resource accounting.
The appendices provide supporting reference material, including brief refreshers on quantum computing fundamentals and curated overviews of problem landscapes with quantum potential.
For print production, this single book is issued as two physical volumes due to length limits. Volume 1 contains Parts I–II, and Volume 2 contains Parts III–IV and the appendices.
