Quantum Mechanics And Algorithms by Yair Shapira (.PDF)
File Size: 15.0 MB
Quantum Mechanics And Algorithms: An Algebraic-geometric Perspective by Yair Shapira
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Overview: This book introduces quantum mechanics from an algebraic-geometrical point of view. This puts quantum mechanics quite firmly on top of three mathematical legs: linear algebra, calculus, and geometry. Thanks to the new geometrical picture, physics follows naturally from math. Not only that: quantum mechanics is well-embedded in science and technology. For example, the book uses quantum mechanics to develop quantum algorithms, including quantum FFT and Shor’s factoring algorithm in cryptography. After introducing quantum mechanics from scratch, the discussion follows to entropy with a focus on entanglement entropy. Moreover, the algebraic study of angular momentum and energy helps analyse spin and polarization alike. Next, the book introduces algorithms in cryptography, where quantum algorithms are particularly relevant. Finally, Feynman diagrams are also introduced from an algebraic perspective. The book ends with examples of how practical algorithms are programmed on the computer. This book contains seven parts. Part I introduces quantum mechanics from scratch and illustrates its dynamics in our new time–energy coordinates. Moreover, it highlights the principle of minimum energy, useful in Machine Learning and image processing too. Part II introduces entropy in physics and computing, including entanglement entropy. Part III introduces spin and polarization, useful in quantum computing too. Part IV introduces practical algorithms in cryptography. Part V introduces important quantum algorithms that have a potential to transform the entire field of cryptography. Part VI introduces Feynman diagrams algebraically geometrically, with elements from quantum field theory. Finally, Part VII implements a few practical algorithms in C++, with a complete code, explained in detail, line by line.
Genre: Non-Fiction > Tech & Devices
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