Introduction to Quantum Computing

This textbook introduces quantum computing to readers who do not have much background in linear algebra. The author targets undergraduate and master students, as well as non-CS and non-EE students who are willing to spend about 60 -90 hours seriously learning quantum computing. Readers will be able to write their program to simulate quantum computing algorithms and run on real quantum computers on IBM-Q. Moreover, unlike the books that only give superficial, "hand-waving" explanations, this book uses exact formalism so readers can continue to pursue more advanced topics based on what they learn from this book.

The Most Important Step to Understand Quantum Computing.- First Impression.- Basis, Basis Vectors, and Inner Product.- Orthonormal Basis, Bra-Ket Notation, and Measurement.- Changing Basis, Uncertainty Principle, and Bra-ket Operations.- Observables, Operators, Eigenvectors, and Eigenvalues.- Pauli Spin Matrices, Adjoint Matrix, and Hermitian Matrix.- Operator Rules, Real Eigenvalues, and Projection Operator.- Eigenvalue and Matrix Diagonalization; Unitary Matrix.- Unitary Transformation, Completeness, and Construction of Operator.- Hilbert Space, Tensor Product, and Multi-Qubit.- Tensor Product of Operators, Partial Measurement, and Matrix Representation in a Given Basis.- Quantum Register and Data Processing, Entanglement and the Bell States.- Concepts Review, Density Matrix, and Entanglement Entropy.- Quantum Gate Introduction; NOT and C-NOT Gates.- SWAP, Phase Shift and CC-NOT (Toffoli) Gates.- Walsh-Hadamard Gate and its Properties.- 13 more chapters.