Mathematical Foundations of Quantum Computing: A Scaffolding Approach (The Scaffolding Series) - Softcover

Lee, Peter Y.; Yu, James M.; Cheng, Ran

Softcover

ISBN 10: 1961880091 ISBN 13: 9781961880092

Publisher: Polaris QCI Publishing, 2025

Synopsis

Essential Mathematics for Quantum Computing
This focused guide connects key mathematical principles with their specialized applications in quantum computing, equipping students with the essential tools to succeed in this transformative field. It is ideal for educators, students, and self-learners seeking a strong mathematical foundation to master quantum mechanics and quantum algorithms.
Features

• Covers key mathematical concepts, including matrix algebra, probability, and Dirac notation, tailored for quantum computing.
• Explains essential topics like tensor products, matrix decompositions, Hermitian and unitary matrices, and their roles in quantum transformations.
• Offers a streamlined introduction to foundational math topics for quantum computing, with an emphasis on accessibility and application.

Authors

• Dr. Peter Y. Lee (Ph.D., Princeton University) – Expert in quantum nanostructures with extensive experience in teaching and academic program leadership.
• James M. Yu (Ph.D., Rutgers University) – Expert in mathematical modeling, applied mathematics, and quantum computing, with extensive teaching experience.
• Dr. Ran Cheng (Ph.D., University of Texas at Austin) – Specialist in condensed matter theory and an award-winning physicist.

About this title

About the Author

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.
James M. Yu: Earned his Ph.D. in Mechanical Engineering from Rutgers University at New Brunswick, specialized in mathematical modeling and simulation of biophysical phenomena. Following his doctorate studies, he continued to conduct research as a postdoctoral associate at Rutgers University. Currently, he is a faculty member at Fei Tian College, Middletown, where he dedicates his time to teaching mathematics, statistics, and computer science.
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.

• Covers key mathematical concepts, including matrix algebra, probability, and Dirac notation, tailored for quantum computing.
• Explains essential topics like tensor products, matrix decompositions, Hermitian and unitary matrices, and their roles in quantum transformations.
• Offers a streamlined introduction to foundational math topics for quantum computing, with an emphasis on accessibility and application.

Authors

• Dr. Peter Y. Lee (Ph.D., Princeton University) - Expert in quantum nanostructures with extensive experience in teaching and academic program leadership.
• James M. Yu (Ph.D., Rutgers University) - Expert in mathematical modeling, applied mathematics, and quantum computing, with extensive teaching experience.
• Dr. Ran Cheng (Ph.D., University of Texas at Austin) - Specialist in condensed matter theory and an award-winning physicist.

From the Inside Flap

A Journey Well Traveled
Congratulations to all who have completed this book, especially those who engaged with the exercises and problems throughout. You've successfully established a strong foundation in the mathematical concepts underpinning quantum computing, equipping yourselves for further exploration in this rapidly advancing field.
The Mathematical Horizon
As quantum computing continues to evolve, so too does its mathematical framework. New discoveries in areas such as quantum algorithms, cryptography, and error correction challenge us to deepen our mathematical understanding and extend it into new realms. The foundational topics you have mastered—linear algebra, Dirac notation, matrix analysis, and probability—will remain central as quantum technology progresses.
But there are still many exciting mathematical challenges ahead. As the quest for quantum algorithms and scalable, fault-tolerant quantum computing continues, new theoretical tools will be required. Quantum computing presents unique mathematical demands, and the journey ahead will offer opportunities to expand upon the knowledge you have gained here.
Looking Forward
As you continue your journey, consider the following next steps:

• Study the fundamentals of quantum computing and information, by exploring the second book in this series, Quantum Computing and Information: A Scaffolding Approach.
• Delve into quantum algorithms after establishing a solid understanding of quantum computing, as these offer solutions across a wide range of applications.
• Explore other fields within quantum science, such as quantum sensing, where new frontiers in technology and mathematics are rapidly emerging.
• Stay updated with the latest advancements in quantum computing, including hardware innovations, error correction techniques, and emerging algorithms.

With the knowledge gained from this book, you are well-positioned to further explore the fascinating realm of quantum computing and related fields. Keep learning, stay curious, and continue to expand your understanding of this ever-evolving subject.

Edition details

• Publisher: Polaris QCI Publishing
• Publication date: 2025
• ISBN 10: 1961880091
• ISBN 13: 9781961880092
• Binding: Paperback
• Language: English
• Number of pages: 572