Quantum Algorithms and Applications: Book Information

Unlock the Potential of Quantum Algorithms

This book presents a progressive scaffolding approach to quantum algorithms and applications, guiding readers from core primitives to practical workflows in simulation, optimization, quantum machine learning, and linear systems, with an emphasis on mastering durable concepts and principles.

Features

• A systematic, student-friendly route through quantum algorithms.
• Comprehensive coverage, from core primitives to real applications.
• Up to date: QSVT, SQD, QML, classical shadows, differential-equation solvers, and the quest for quantum advantage.

Authors

• Dr. Peter Y. Lee (Ph.D., Princeton University) – Expert in quantum nanostructures with extensive experience in teaching and academic program leadership.
• Dr. Ran Cheng (Ph.D., University of Texas at Austin) – Specialist in condensed matter theory and an award-winning physicist.
• Dr. Huiwen Ji (Ph.D., Princeton University) – Accomplished researcher with a solid background in quantum chemistry and numerous awards.

• ISBN 978-1-961880-11-5 (vol 1+2 combined, ebook, color)
• ISBN 978-1-961880-12-2 (vol 1, paperback, b/w)
• ISBN 978-1-961880-13-9 (vol 2, paperback, b/w)
• ISBN 978-1-961880-14-6 (vol 1, hardcover, b/w)
• ISBN 978-1-961880-15-3 (vol 2, hardcover, b/w)

Quantum Algorithms and Applications: A Scaffolding Approach develops quantum computing through the lens of algorithms and the workflows they enable. It guides readers in a carefully staged progression from core primitives—such as Fourier-based methods, amplitude techniques, Hamiltonian simulation, and modern polynomial-approximation frameworks including block encoding and quantum singular value transformation—to practical application motifs in physics and chemistry simulation, optimization, quantum machine learning, and quantum methods for linear systems and differential equations.

Throughout, the emphasis is on mastering durable concepts and principles: what is being computed, what is assumed about data access and outputs, how resources and error shape performance, and how to evaluate claims of quantum advantage with clarity. The book is written for senior undergraduates, beginning graduate students, and practitioners, and is reinforced with in-text exercises, end-of-chapter problem sets, and recurring design patterns that help readers build a coherent, long-lasting mental model of quantum computation.

• Pedagogically sound approach
• Up-to-date information
• Navigational aids
• Clean and clear layout
• Engaging exercises
• Suitable for senior undergraduates and early graduates
• 700 pages, 100+ illustrations

Dr. Peter Y. Lee holds a Ph.D. in Electrical Engineering from Princeton University. His research at Princeton focused on quantum nanostructures, the fractional quantum Hall effect, and Wigner crystals. Following his academic tenure, he joined Bell Labs, making significant contributions to the fields of photonics and optical communications and securing over 20 patents. Dr. Lee's multifaceted expertise extends to educational settings; he has a rich history of teaching, academic program oversight, and computer programming.

Dr. Ran Cheng earned his Ph.D. in Physics from the University of Texas at Austin, with a specialization in condensed matter theory, particularly in spintronics and magnetism. Following a postdoctoral position at Carnegie Mellon University, he joined the faculty at the University of California, Riverside, where he was honored with the NSF CAREER and DoD MURI awards.

Dr. Huiwen Ji holds a Ph.D. in Chemistry from Princeton University. She is a materials chemist whose research spans solid-state functional materials, quantum materials, and energy-related materials. After appointments at the University of California, Berkeley and Lawrence Berkeley National Laboratory, she joined the University of Utah as a faculty member in Materials Science and Engineering. Her honors include an NSF CAREER Award.

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.

VOLUME 1

Part I Foundations of Quantum Algorithms
1 Algorithmic Thinking
2 Quantum Algorithms: A New Paradigm
3 Quantum Circuit Model and Query Model
4 Classification of Computational Complexity
5 FTQC vs. NISQ Algorithms

Part II Core Quantum Algorithms
6 Quantum Fourier Transform (QFT)
7 Quantum Phase Estimation (QPE)
8 Shor’s Algorithm and Period Finding
9 Amplitude Amplification and Estimation
10 Foundations of Hamiltonian Simulation
11 Polynomial Approximation Algorithms
12 Quantum Linear System Algorithms (QLSA)
13 Adiabatic and Variational Quantum Algorithms
14 Measurement Primitives

VOLUME 2

Part III Quantum Physics & Chemistry Simulations
15 Simulation Formulations and Encodings
16 Foundations of Quantum Chemistry Simulations
17 Static Properties and Spectra
18 Dynamics and Correlation Functions
19 Many-Body and Materials Models

Part IV Other Applications
20 Quantum Optimization and Heuristics
21 Quantum Machine Learning
22 Quantum Solvers for Differential Equations
23 The Quest for Quantum Advantage

Part V Supporting Materials
Appendices
A Quantum Computing Fundamentals
B Error Correction and Fault-Tolerance Formalism
C Quantum Software Platforms and Frameworks
D 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.