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2022 | Buch

The Most Important Step to Understand Quantum Computing Kapitel lesen Erstes Kapitel lesen

Introduction to Quantum Computing

From a Layperson to a Programmer in 30 Steps

verfasst von: Hiu Yung Wong

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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SUCHEN

Über dieses Buch

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.Encourages students to embrace uncertainty over the daily classical experience, when encountering quantum phenomena;Uses narrative to start each section with analogies that help students to grasp the critical concept quickly;Uses numerical substitutions, accompanied by Python programming and IBM-Q quantum computer programming, as examples in teaching all critical concepts.

Inhaltsverzeichnis

Frontmatter

Linear Algebra for Quantum Computing

Frontmatter
Chapter 1. The Most Important Step to Understand Quantum Computing
Abstract
Know when to believe and when to question.
Hiu Yung Wong
Chapter 2. First Impression
Abstract
Have an idea of how quantum computing is different from classical computing; Gain first impressions of the keywords in quantum computing.
Hiu Yung Wong
Chapter 3. Basis, Basis Vectors, and Inner Product
Abstract
Understand the concept of basis; Be familiar with vector inner product; Reinforce the concept of vector representations; Be comfortable when dealing with hyperspaces that we cannot feel.
Hiu Yung Wong
Chapter 4. Orthonormal Basis, Bra–Ket Notation, and Measurement
Abstract
Understand that orthonormal bases and normalized vectors are used in quantum computing; Have a deeper understanding of Bra–Ket notation; Understand the meaning of superposition coefficient in measurement.
Hiu Yung Wong
Chapter 5. Changing Basis, Uncertainty Principle, and Bra–Ket Operations
Abstract
Know how to represent vectors in different bases; Have a feeling on the origin of the uncertainty principle; Be more familiar with Bra–Ket operations.
Hiu Yung Wong
Chapter 6. Observables, Operators, Eigenvectors, and Eigenvalues
Abstract
Understand the connections between operator matrices and observables; Able to find the eigenvalues and eigenvectors of a matrix.
Hiu Yung Wong
Chapter 7. Pauli Spin Matrices, Adjoint Matrix, and Hermitian Matrix
Abstract
Be familiar with Pauli matrices and Pauli vector and their properties; Be familiar with matrix-vector multiplications; Understand the importance of adjoint and Hermitian matrices.
Hiu Yung Wong
Chapter 8. Operator Rules, Real Eigenvalues, and Projection Operator
Abstract
Understand the rules of manipulating operators in the bra and ket spaces; Appreciate the importance of Hermitian matrices and their relationship to observables; Have an intuitive understanding of projection operators; Understand the difference between inner and outer products.
Hiu Yung Wong
Chapter 9. Eigenvalue, Matrix Diagonalization and Unitary Matrix
Abstract
Understand the meaning of matrix diagonalization and its equivalence to finding eigenvalues and eigenvectors; able to find eigenvalues and eigenvectors; understand the importance of unitary matrix and its properties.
Hiu Yung Wong
Chapter 10. Unitary Transformation, Completeness, and Construction of Operator
Abstract
Able to perform unitary transformation; able to construct unitary transformation matrix from the given bases; be prepared to use the completeness equation for quantum computing; able to construct operator from the given eigenvectors and eigenvalues.
Hiu Yung Wong
Chapter 11. Hilbert Space, Tensor Product, and Multi-Qubit
Abstract
Have an idea that Hilbert space is just an extension of the real space; understand that tensor product is a way to construct a higher-dimensional Hilbert space from lower ones; appreciate the power of quantum computing due to the tensor product of qubits; familiar with important tensor product operations.
Hiu Yung Wong
Chapter 12. Tensor Product of Operators, Partial Measurement, and Matrix Representation in a Given Basis
Abstract
Be more skillful in tensor product operations; understand how to perform tensor product for matrices; understand the meaning of partial measurement and normalization after measurement; understand the meaning of the operator matrix elements in a given basis.
Hiu Yung Wong

Quantum Computing: Gates and Algorithms

Frontmatter
Chapter 13. Quantum Register and Data Processing, Entanglement, the Bell States, and EPR Paradox
Abstract
Understand the similarity and difference between a quantum register and a classical register; be more familiar with the tensor and inner products between multiple qubits; better understanding on why the quantum computer is powerful; understand entanglement and the Bell States; appreciate Einstein–Podolsky–Rosen (EPR) paradox.
Hiu Yung Wong
Chapter 14. Concepts Review, Density Matrix, and Entanglement Entropy
Abstract
Have a deeper understanding of the linear algebra and quantum mechanics concepts and skills; able to understand and apply the basic concepts and skills in advanced examples; understand the difference between pure and mixed states; and know how to calculate the density matrix and entanglement entropy.
Hiu Yung Wong
Chapter 15. Quantum Gate Introduction: NOT and CNOT Gates
Abstract
Understand how a quantum gate is related to the physics underneath; understand how a quantum gate is different from a classical gate; able to describe the matrix and properties of NOT and C-NOT gates; and understand the relationship between a quantum gate and its corresponding classical gate.
Hiu Yung Wong
Chapter 16. SWAP, Phase Shift, and CCNOT (Toffoli) Gates
Abstract
Able to describe the matrix and properties of SWAP, Phase Shift, and CCNOT gates.
Hiu Yung Wong
Chapter 17. Walsh–Hadamard Gate and Its Properties
Abstract
Understand that the Walsh-Hadamard gate has no classical counterpart; Remember the special properties of the Walsh-Hadamard gate; Familiar with the mathematical skills for deriving the Walsh-Hadamard gate properties.
Hiu Yung Wong
Chapter 18. Two Quantum Circuit Examples
Abstract
Able to describe the meaning of little-endian convention; Be aware of the existence of big-endian convention; Contrast the flow direction of the vector in an equation and a circuit; Able to construct a quantum circuit based on a given simple equation; Able to understand a quantum circuit through both matrix method and intuition.
Hiu Yung Wong
Chapter 19. No-Cloning Theorem and Quantum Teleportation I
Abstract
Able to prove No-Cloning Theorem and describe which type of quantum states cannot be cloned; Understand quantum teleportation and compare against “real” teleportation; Understand the limitation of the simplified version of quantum teleportation; Know how to measure a qubit in its https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-98339-0_19/524396_1_En_19_IEq1_HTML.gif basis using the apparatus in the https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-98339-0_19/524396_1_En_19_IEq2_HTML.gif basis.
Hiu Yung Wong
Chapter 20. Quantum Teleportation II and Entanglement Swapping
Abstract
Describe the role of the ancillary bit in the complete version of quantum teleportation; Construct the quantum teleportation circuit on IBM-Q; Apply quantum teleportation circuit to achieve entanglement swapping; Understand deeper how to use the classical register in a conditional quantum gate.
Hiu Yung Wong
Chapter 21. Deutsch Algorithm
Abstract
Understand the Deutsch–Jozsa and Deutsch problems; Appreciate how quantum parallelism is used to speed up the solution-finding process in the Deutsch algorithm; Understand while parallel computations are performed in certain quantum algorithms, the information we can extract is limited. Understand the origin of the quantum oracle; Able to derive the equations in the Deutsch algorithm and implement them in IBM-Q.
Hiu Yung Wong
Chapter 22. Quantum Oracles and Construction of Quantum Gate Matrices
Abstract
Able to distinguish the two types of quantum oracles, namely the XOR and phase quantum oracles; Able to explain why a quantum oracle needs to be unitary and reversible; Able to construct the matrix of any quantum gate when the definition is given.
Hiu Yung Wong
Chapter 23. Grover’s Algorithm: I
Abstract
Able to perform simple computational complexity analysis; Understand the meaning of exponential and quadratic speedups; Understand the concept of basis encoding; Able to describe the meanings and roles of the three important vectors and the two important matrices in Grover’s algorithm; Able to explain Grover’s algorithm pictorially.
Hiu Yung Wong
Chapter 24. Grover’s Algorithm: II
Abstract
Gain a deeper understanding of Grover’s algorithm; Able to perform numerical substitutions; Able to construct the algorithm on IBM-Q and analyze the data; Able to contrast the difference between a phase quantum oracle and an XOR quantum oracle in Grover’s algorithm and how they affect the quantum circuit construction.
Hiu Yung Wong
Chapter 25. Quantum Fourier Transform I
Abstract
Able to describe some important identities of the N-th root of unity; can describe the differences and similarities between Discrete Fourier Transform and Quantum Fourier Transform; able to describe inverse Quantum Fourier Transform; understand why Quantum Fourier Transform gate is unitary and symmetric.
Hiu Yung Wong
Chapter 26. Quantum Fourier Transform II
Abstract
Have a deeper appreciation of the difference between basis transformation and vector transformation; be aware of the existence of the two definitions of QFT that are inverse of the other; understand how to construct an n-qubit SWAP gate; able to construct a 3-qubit QFT circuit and run on IBM-Q.
Hiu Yung Wong
Chapter 27. Bloch Sphere and Single-Qubit Arbitrary Unitary Gate
Abstract
Able to describe how to map a qubit state to the surface of the Bloch sphere; able to perform rotation on the Bloch sphere for a given set of Euler angles; be aware of the correct and incorrect relationship between the qubit space and the real 3D space; able to construct arbitrary unitary rotation using the U θ,ϕ,λ gate.
Hiu Yung Wong
Chapter 28. Quantum Phase Estimation
Abstract
Understand the four parameters in the general controlled unitary gate; able to describe the meaning of the qubits in the Quantum Phase Estimation (QPE) algorithm; able to explain the gates needed to construct a QPE circuit; understand mathematically how QPE works; able to implement and inspect the hardware results of QPE.
Hiu Yung Wong
Chapter 29. Shor’s Algorithm
Abstract
Understand the role of Shor’s algorithm in the prime integer factorization process and its relationship to encryption; able to derive and explain the equations in the Shor’s algorithm; appreciate that Shor’s algorithm is the type of quantum algorithm that does not give deterministic results and needs trials and errors, but the results can be verified easily.
Hiu Yung Wong
Chapter 30. The Last But Not the Least
Abstract
Understand how to practice quantum programming; understand what you do not know.
Hiu Yung Wong
Backmatter
Metadaten
Titel
Introduction to Quantum Computing
verfasst von
Hiu Yung Wong
Copyright-Jahr
2022
Electronic ISBN
978-3-030-98339-0
Print ISBN
978-3-030-98338-3
DOI
https://doi.org/10.1007/978-3-030-98339-0

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