Quantum Computing for Engineers

This book is a practical guide for students and engineers eager to dive into the rapidly emerging field of quantum computing and harness its transformative power to tackle complex engineering and scientific challenges. It offers a clear and detailed analysis of cutting-edge quantum algorithms for problems of real-world importance such as linear systems and differential equations and demonstrates the remarkable speedups and capabilities unlocked by quantum computers.

Readers will gain a solid grasp of how quantum algorithms work under the hood and will be well-equipped to navigate the exciting paradigm shift in scientific and engineering computation driven by the quantum revolution whether through designing new quantum algorithms for targeted applications or by developing a broad understanding of the emerging quantum landscape. The book includes hands-on example code and problem sets to bridge theory and practice.

Part 1. - 1. Linear Algebra and Probability. - 2. Polynomial Approximations. - 3. Theory of Computing. - 4. An Overview of Practical Classical Computing. - 5. Information and Complexity Theory. - Part II. - 6. A Gentle Introduction to Quantum Mechanics. - 7. The Stern-Gerlach Experiment. - 8. Photon Polarization. - Part III. - 9. Qubits, Quantum Registers, and Quantum Gates. - 10. Quantum Measurements and Circuits. - 11. Superposition and Entanglement. - 12. Classical and Reversible Computation. - 13. Access Models and Data Representation. - 14. Limitations of Quantum Computers. - 15. Simon s, Deutsch-Jozsa, and Bernstein-Vazirani Algorithms. - Part IV. - 16. The Quantum Computing Stack. - 17. Libraries for Quantum Computing. - Part V. - 18. Phase Kickback. - 19. Quantum Fourier Transform. - 20. Quantum Phase Estimation. - 21. Trotterization. - 22. Linear Combination of Unitaries. - 23. Qubitization and Quantum Signal Processing. - 24. Amplitude Amplification and Estimation. - 25. Quantum Monte Carlo. - 26. Matrix-Vector Multiplications and Affine Linear Operations. - Part VI. - 27. Expectation Value Estimation. - 28. Hamiltonian Simulation Techniques. - 29. Eigenvalue Problems. - 30. Quantum Linear System Algorithms: Direct Methods. - 31. Quantum Linear System Algorithms: Iterative Methods. - 32. Quantum Ordinary Differential Equation Algorithms: Block-matrix algorithms. - 33. Quantum Ordinary Differential Equation Algorithms: Time-marching algorithms. - 34. Quantum Partial Differential Equation Algorithms. - 35. Variational Algorithms: Theory. - 36. Notable Variational Algorithms: VQE, QAOA, VQLS. - Part VII. - 37. Applications in Engineering and Scientific Computing. - 38. Quantum Machine Learning. - 39. Applications in Finance.