Quantum Computing and Quantum Physics A Linear Algebra Approach

Quantum Computing and Quantum Physics: A Linear Algebra Approach provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science and quantum computing.

While broadly accessible, the textbook does not dodge providing a solid conceptual and formal understanding of quantum states, superposition, and entanglement-the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling many of the classic quantum algorithms that demonstrate how and when Quantum Computing has an advantage over classical computers.

The book includes pedagogical features such as 'Try It' boxes, brief exercises that engage the readers and help them digest the many counter-intuitive quantum information science and quantum computing concepts. Self-contained chapters on time dependence in quantum mechanics, magnetic resonance, density matrices, the simple harmonic oscillator, quantum perturbation theory, and number operators provide a basis for further reading and work in quantum information science and quantum computing.

Aimed at undergraduate students with little or no background in physics, but with some familiarity with linear algebra, the book will also appeal to higher education faculty members and secondary school mathematics, physics, and computer science educators who want to learn about quantum computing and perhaps teach a course accessible to students with wide ranging backgrounds.

Alice Flarend, Physics Teacher, Bellwood-Antis High School,Robert Hilborn, Research Affiliate, University of Maryland

Alice Flarend, a former nuclear engineer, earned a PhD in Curriculum and Instruction from the Pennsylvania State University and has been a high school physics teacher for 30 years. She was awarded AAPT's Paul W. Zitzewitz Excellence in K-12 Teaching Award in 2023. Her research interests include making quantum physics accessible to the K-12 classroom and how teachers learn new content and pedagogy, especially in creating a discourse rich classroom. Dr Flarend has two decades of experience providing teacher professional development in physics including classical, nuclear and quantum physics.


Robert Hilborn received his PhD in physics from Harvard University in 1971. He served as a physics faculty member at Oberlin College, Amherst College, the University of Nebraska-Lincoln, and the University of Texas at Dallas. He has had many decades of experience doing quantum physics research in atomic, molecular, and optical physics and teaching quantum mechanics to undergraduate students. He is author of Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers (OUP 1994). He recently retired as the Associate Executive Officer of the American Association of Physics Teachers, where he was principal investigator for several nation-wide physics education projects funded by the National Science Foundation.

Part I: Quantum State and Quantum Information Science Fundamentals1. Introduction2. Traditional Computing3. Traditional Bits in New Clothing4. Qubits and Quantum States5. Quantum Measurements6. Quantum Gates and Quantum Circuits7. Putting a Spin on Spin8. My Basis, Your BasisPart II: Multi-Qubit States9. Multi-Qubit Systems, Entanglement, and Quantum Weirdness10. Quantum Circuits and Multi-Qubit ApplicationsPart III: Quantum Algorithms11. Quantum Computing Algorithms12. More Quantum Algorithms13. Error Correction14. RSA Encryption and Number Theory15. Shor Factoring Algorithm and the Quantum Fourier Transform16. Programming Quantum ComputersPart IV: Deeper Dive into Quantum Mechanics17. Fundamental Quantum Issues18. Quantum State Time Dependence19. Magnetic Precession and Resonance for a Spin-½ System20. Number Operators and Number States21. Momentum and Position Operators and the Simple Harmonic Oscillator22. Density Operators and Density Matrices23. Quantum Perturbation TheoryPart V: Looking to the Future24. Present and Future QIS and QCAppendix: Quantum Toolkit