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kasirajan venkateswaran - fundamentals of quantum computing

Fundamentals of Quantum Computing Theory and Practice




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 06/2021
Edizione: 1st ed. 2021





Trama

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-p 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.





Sommario

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 Operators
2.1 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 Variances
2.8 Eigenstates, Eigenvalues and Eigenfunctions
2.9 Characteristic Polynomial
2.10 Definite Symmetric Matrices
2.11 Tensors
2.12 Statistics and Probability
2.13 Summary
2.14 Practice problems
2.15 References and further reading
3 The Quantum Superposition Principle and Bloch Sphere Representation
3.1 Euclidian Space
3.2 Metric Space
3.3 Hilbert space.
3.4 Schrodinger Equation
3.5 Postulates of Quantum Mechanics
3.6 Quantum Tunneling
3.7 Stern and Gerlach Experiment
3.8 Bloch sphere representation
3.9 Projective Measurements
3.10 Qudits
3.11 Summary
3.12 Practice Problems
3.13 References and further reading
PART TWO
4 Qubit Modalities
4.1 The vocabulary of quantum computing
4.2 Classical Computers – a recap
4.3 Qubits and usability
4.4 Noisy Intermediate Scale Quantum Technology
4.5 Qubit Metrics
4.6 Leading Qubit Modalities
4.7 A note on the dilution refrigerator
4.8 Summary
4.9 Practice Problems
4.10 References and further reading
5 Quantum Circuits and DiVincenzo Criteria
5.1 Setting up the development environment
5.2 Learning Quantum Programming Languages
5.3 Introducing Quantum Circuits
5.4 Quantum Gates
5.5 The Compute Stage
5.6 Quantum Entanglement
5.7 No-Cloning theorem
5.8 Quantum Teleportation
5.9 Superdense coding
5.10 Greenberger–Horne–Zeilinger state (GHZ state)
5.11 Walsh-Hadamard Transform
5.12 Quantum Interference
5.13 Phase kickback
5.14 DiVincenzo’s criteria for quantum computation
5.15 Summary
5.16 Practice Problems
5.17 References and further reading
6 Quantum Communications
6.1 EPR Paradox
6.2 Density Matrix Formalism
6.3 Von Neumann Entropy
6.4 Photons
6.5 Quantum Communication
6.6 The Quantum Channel
6.7 Quantum Communication Protocols
6.8 RSA Security
6.9 Summary
6.10 Practice Problems
6.11 References and further reading
7 Quantum Algorithms
7.1 Quantum Ripple Adder Circuit
7.2 Quantum Fourier Transformation
7.3 Deutsch-Jozsa oracle
7.4 The Bernstein-Vazirani Oracle
7.5 Simon’s algorithm
7.6 Quantum arithmetic using QFT
7.7 Modular exponentiation
7.8 Grover’s search algorithm
7.9 Shor’s algorithm
7.10 A quantum algorithm for k-means
7.11 Quantum Phase Estimation (QPE)
7.12 HHL algorithm for solving linear equations
7.13 Quantum Complexity Theory
7.14 Summary
7.15 Practice Problems
7.16 References and further reading
8 Adiabatic Optimization and Quantum Annealing
8.1 Adiabatic evolution
8.2 Proof of the Adiabatic Theorem
8.3 Adiabatic optimization
8.4 Quantum Annealing
8.5 Summary
8.6 Practice Problems
8.7 References and further reading
9 Quantum Error Correction
9.1 Classical Error Correction
9.2 Quantum Error Codes
9.3 Stabilizer formalism
9.4 The path forward – fault-tolerant quantum computing
9.5 Surface codes
9.6 Protected qubits
9.7 Practice Problems
9.8 References and further reading
10 Conclusion
10.1 How many qubits do we need?
10.2 Classical simulation
10.3 Backends today
10.4 Future state
10.5 References





Autore

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.











Altre Informazioni

ISBN:

9783030636883

Condizione: Nuovo
Dimensioni: 254 x 178 mm Ø 1121 gr
Formato: Copertina rigida
Illustration Notes:XXIX, 463 p. 277 illus., 261 illus. in color.
Pagine Arabe: 463
Pagine Romane: xxix


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