This introductory book on quantum computing includes an emphasis on the development of algorithms. Appropriate for both university students as well as software developers interested in programming a quantum computer, this practical approach to modern quantum computing takes the reader through the required background and up to the latest developments.
Beginning with introductory chapters on the required math and quantum mechanics, Fundamentals of Quantum Computing proceeds to describe four leading qubit modalities and explains the core principles of quantum computing in detail. Providing a step-by-step derivation of math and source code, some of the well-known quantum algorithms are explained in simple ways so the reader can try them either on IBM Q or Microsoft QDK. The book also includes a chapter on adiabatic quantum computing and modern concepts such as topological quantum computing and surface codes.
Features:
o Foundational chapters that build the necessary background on math and quantum mechanics.
o Examples and illustrations throughout provide a practical approach to quantum programming with end-of-chapter exercises.
o Detailed treatment on four leading qubit modalities -- trapped-ion, superconducting transmons, topological qubits, and quantum dots -- teaches how qubits work so that readers can understand how quantum computers work under the hood and devise efficient algorithms and error correction codes. Also introduces protected qubits - 0- qubits, fluxon parity protected qubits, and charge-parity protected qubits.
o Principles of quantum computing, such as quantum superposition principle, quantum entanglement, quantum teleportation, no-cloning theorem, quantum parallelism, and quantum interference are explained in detail.
A dedicated chapter on quantum algorithm explores both oracle-based, and Quantum Fourier Transform-based algorithms in detail with step-by-step math and working code that runs on IBM QisKit and Microsoft QDK. Topics on EPR Paradox, Quantum Key Distribution protocols, Density Matrix formalism, and Stabilizer formalism are intriguing. While focusing on the universal gate model of quantum computing, this book also introduces adiabatic quantum computing and quantum annealing.
This book includes a section on fault-tolerant quantum computing to make the discussions complete. The topics on Quantum Error Correction, Surface codes such as Toric code and Planar code, and protected qubits help explain how fault tolerance can be built at the system level.
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 Theorem8.3 Adiabatic optimization8.4 Quantum Annealing8.5 Summary8.6 Practice Problems8.7 References and further reading9 Quantum Error Correction9.1 Classical Error Correction9.2 Quantum Error Codes9.3 Stabilizer formalism9.4 The path forward - fault-tolerant quantum computing9.5 Surface codes9.6 Protected qubits9.7 Practice Problems9.8 References and further reading10 Conclusion10.1 How many qubits do we need?10.2 Classical simulation10.3 Backends today10.4 Future state10.5 References
Venkateswaran Kasirajan (Venkat) is an Engineering Director at Trimble, Inc., overseeing a high-profile engineering team. By being a part of two startups, Venkat had the opportunity to work on several core technologies and booted the career of hundreds of engineers. He was also involved in several patents.
Before studying computer science and taking up a software engineering career, Venkat studied physics; and currently continues his interest in condensed matter physics. He also researches quantum algorithms and topology, and serves as an internal champion for quantum computing at Trimble Inc. When not working, Venkat is either listening to country music or teaching his daughter while living with his family in Colorado, USA.
