Mathematical Foundations of Quantum Computing: A Scaffolding Approach

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.

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.