Fundamentals of Quantum Computing: Theory and Practice

PART ONE 1 Foundations of Quantum Mechanics 1.1 Matter 1.2 Atoms, Elementary Particles, and Molecules 1.3 Light and Quantization of Energy 1.4 Electron Configuration 1.5 Wave-Particle Duality and Probabilistic Nature 1.6 Wavefunctions and Probability Amplitudes 1.7 Some exotic states of matter 1.8 Summary 1.9 Practice Problems 1.10 References and further reading 2 Dirac's bra-ket notation and Hermitian Operators2.1 Scalars 2.2 Complex Numbers 2.3 Vectors 2.4 Matrices 2.5 Linear Vector Spaces 2.6 Using Dirac's bra-ket notation 2.7 Expectation Values and Variances2.8 Eigenstates, Eigenvalues and Eigenfunctions2.9 Characteristic Polynomial 2.10 Definite Symmetric Matrices 2.11 Tensors2.12 Statistics and Probability2.13 Summary 2.14 Practice problems2.15 References and further reading3 The Quantum Superposition Principle and Bloch Sphere Representation3.1 Euclidian Space3.2 Metric Space3.3 Hilbert space.3.4 Schrodinger Equation3.5 Postulates of Quantum Mechanics3.6 Quantum Tunneling3.7 Stern and Gerlach Experiment3.8 Bloch sphere representation3.9 Projective Measurements3.10 Qudits3.11 Summary3.12 Practice Problems3.13 References and further readingPART TWO4 Qubit Modalities4.1 The vocabulary of quantum computing4.2 Classical Computers - a recap 4.3 Qubits and usability4.4 Noisy Intermediate Scale Quantum Technology4.5 Qubit Metrics4.6 Leading Qubit Modalities4.7 A note on the dilution refrigerator4.8 Summary4.9 Practice Problems4.10 References and further reading5 Quantum Circuits and DiVincenzo Criteria5.1 Setting up the development environment5.2 Learning Quantum Programming Languages 5.3 Introducing Quantum Circuits 5.4 Quantum Gates 5.5 The Compute Stage5.6 Quantum Entanglement5.7 No-Cloning theorem5.8 Quantum Teleportation5.9 Superdense coding5.10 Greenberger-Horne-Zeilinger state (GHZ state)5.11 Walsh-Hadamard Transform5.12 Quantum Interference5.13 Phase kickback5.14 DiVincenzo's criteria for quantum computation5.15 Summary 5.16 Practice Problems5.17 References and further reading6 Quantum Communications6.1 EPR Paradox6.2 Density Matrix Formalism6.3 Von Neumann Entropy6.4 Photons6.5 Quantum Communication6.6 The Quantum Channel6.7 Quantum Communication Protocols6.8 RSA Security6.9 Summary6.10 Practice Problems6.11 References and further reading7 Quantum Algorithms7.1 Quantum Ripple Adder Circuit7.2 Quantum Fourier Transformation7.3 Deutsch-Jozsa oracle7.4 The Bernstein-Vazirani Oracle7.5 Simon's algorithm7.6 Quantum arithmetic using QFT7.7 Modular exponentiation7.8 Grover's search algorithm 7.9 Shor's algorithm7.10 A quantum algorithm for k-means7.11 Quantum Phase Estimation (QPE)7.12 HHL algorithm for solving linear equations7.13 Quantum Complexity Theory7.14 Summary 7.15 Practice Problems7.16 References and further reading8 Adiabatic Optimization and Quantum Annealing8.1 Adiabatic evolution8.2 Proof of the Adiabatic Theorem