Introduction to Quantum Computing: From a Layperson to a Programmer in 30 Steps

Preface
Contents
Part I Linear Algebra for Quantum Computing
	1 The Most Important Step to Understand Quantum Computing
		1.1 Learning Outcomes
		1.2 How to Learn Quantum Computing
	2 First Impression
		2.1 Learning Outcomes
		2.2 What Is Quantum Computing?
		2.3 Summary
		Problems
	3 Basis, Basis Vectors, and Inner Product
		3.1 Learning Outcomes
		3.2 A Romantic Story
		3.3 Vectors in Quantum Computing
		3.4 Vector Space
		3.5 Inner Products of Vectors
		3.6 Higher Dimensional Vector Space
		3.7 Summary
		Problems
	4 Orthonormal Basis, Bra–Ket Notation, and Measurement
		4.1 Learning Outcomes
		4.2 Orthonormal Basis
		4.3 Bra–Ket Notation
		4.4 Quantum Mechanical State, Superposition, and Measurement
		4.5 Summary
		Problems
	5 Changing Basis, Uncertainty Principle, and Bra–Ket Operations
		5.1 Learning Outcomes
		5.2 Basis and Uncertainty Principle
		5.3 More Bra–ket Operations
		5.4 Summary
		5.5 More About Python
		Problems
	6 Observables, Operators, Eigenvectors, and Eigenvalues
		6.1 Learning Outcomes
		6.2 Observables and Operators
		6.3 Eigenvalues and Eigenvectors
		6.4 Eigenvalues and Eigenvectors Finding and Phase Factor
		6.5 Remarks on Eigenvectors, Basis, and Measurement
		6.6 Summary
		Problems
	7 Pauli Spin Matrices, Adjoint Matrix, and Hermitian Matrix
		7.1 Learning Outcomes
		7.2 Pauli Spin Matrices
		7.3 Commutation and Anti-commutation
		7.4 Spin Operator in Arbitrary Direction
		7.5 Relationship Between Spin Direction and Real 3D Space
		7.6 Adjoint and Hermitian Matrices
		7.7 Summary
		Problems
	8 Operator Rules, Real Eigenvalues, and Projection Operator
		8.1 Learning Outcomes
		8.2 Operator Rules in the Bra-ket Notation
		8.3 Eigenvalues of Hermitian Matrix
		8.4 Copenhagen Interpretation/Born Rule and Projection Operator
		8.5 Summary
		Problems
	9 Eigenvalue, Matrix Diagonalization and Unitary Matrix
		9.1 Learning Outcomes
		9.2 Eigenvalues and Matrix Diagonalization
		9.3 Unitary Matrix
		9.4 Summary
		Problems
	10 Unitary Transformation, Completeness, and Construction of Operator
		10.1 Learning Outcomes
		10.2 Unitary Transformation
		10.3 Construction of Unitary Transformation Matrices
		10.4 Completeness of Basis
		10.5 Construct Operator from Eigenvalues and Eigenvectors
		10.6 Summary
		Problems
	11 Hilbert Space, Tensor Product, and Multi-Qubit
		11.1 Learning Outcomes
		11.2 Hilbert Space
		11.3 Expansion of Hilbert Space and Tensor Product
		11.4 Multi-Qubits
		11.5 More About Tensor Product in Hilbert Space
		11.6  Summary
		Problems
	12 Tensor Product of Operators, Partial Measurement, and Matrix Representation in a Given Basis
		12.1 Learning Outcomes
		12.2 Tensor Product of Vectors in General Form
		12.3 Tensor Product of Operators
		12.4 Partial Measurement
		12.5 Matrix Representation in a Given Basis
		12.6 Summary
		Problems
Part II Quantum Computing: Gates and Algorithms
	13 Quantum Register and Data Processing, Entanglement, the Bell States, and EPR Paradox
		13.1 Learning Outcomes
		13.2 Quantum Register
		13.3 Quantum Data Processing
		13.4 Entanglement and Bell States
		13.5 Einstein–Podolsky–Rosen (EPR) Paradox
		13.6 Summary
		Problems
	14 Concepts Review, Density Matrix, and Entanglement Entropy
		14.1 Learning Outcomes
		14.2 Concepts Review Using Entanglement
		14.3 Pure State, Mixed State, and Density Matrix
		14.4 Measurement of Entanglement
		14.5 Summary
		Problems
	15 Quantum Gate Introduction: NOT and CNOT Gates
		15.1 Learning Outcomes
		15.2 Basic Quantum Gate Properties
		15.3 NOT (X) Gate
			15.3.1 Definition
			15.3.2 Matrix
			15.3.3 Circuit and Properties
		15.4 XOR (CNOT) Gate
			15.4.1 Definition
			15.4.2 Matrix
			15.4.3 Circuit and Properties
		15.5 Summary
		Problems
	16 SWAP, Phase Shift, and CCNOT (Toffoli) Gates
		16.1 Learning Outcomes
		16.2 SWAP Gate
			16.2.1 Definition
			16.2.2 Matrix
			16.2.3 Circuit and Properties
		16.3 Phase Shift Gate
			16.3.1 Definition
			16.3.2 Matrix
			16.3.3 Circuit and Properties
		16.4 Controlled Phase Shift Gate
			16.4.1 Definition
			16.4.2 Matrix
			16.4.3 Circuit and Properties
		16.5 Toffoli (CCNOT) Gate
			16.5.1 Definition
			16.5.2 Matrix
			16.5.3 Circuit and Properties
		16.6 Summary
		Problems
	17 Walsh–Hadamard Gate and Its Properties
		17.1 Learning Outcomes
		17.2 Walsh–Hadamard Gate
			17.2.1 Definition
			17.2.2 Matrix
			17.2.3 Circuit
		17.3 Properties of the Hadamard Gate
			17.3.1 Inverse of Hadamard Gate
			17.3.2 Multiple-Qubit Hadamard Gate
			17.3.3 Properties of n-Qubit Hadamard Gate
		17.4 Summary
		Problems
	18 Two Quantum Circuit Examples
		18.1 Learning Outcomes
		18.2 Quantum Circuit for Rotating Basis
			18.2.1 Run on IBM-Q
		18.3 Quantum Circuit for Implementing a SWAP Gate
			18.3.1 Run on IBM-Q
		18.4 Summary
		Problems
	19 No-Cloning Theorem and Quantum Teleportation I
		19.1 Learning Outcomes
		19.2 No-Cloning Theorem
		19.3 Quantum Teleportation
			19.3.1 A Simplified Version
			19.3.2 Measurement in the 69640972 +"526930B /69640972 -"526930B  Basis
			19.3.3 Run on IBM-Q
		19.4 Summary
		Problems
	20 Quantum Teleportation II and Entanglement Swapping
		20.1 Learning Outcomes
		20.2 Quantum Teleportation: The Full Version
			20.2.1 Run on IBM-Q
		20.3 Entanglement Swapping
			20.3.1 Run on IBM-Q
		20.4 Summary
		Problems
	21 Deutsch Algorithm
		21.1 Learning Outcomes
		21.2 Deutsch Algorithm
			21.2.1 The Problem
			21.2.2 Classical Algorithm
			21.2.3 Quantum Computing Solution
			21.2.4 The Quantum Circuit
			21.2.5 Run on IBM-Q
		21.3 Summary
		Problems
	22 Quantum Oracles and Construction of Quantum Gate Matrices
		22.1 Learning Outcomes
		22.2 Quantum Oracle
			22.2.1 XOR Quantum Oracle
			22.2.2 Phase Quantum Oracle
		22.3 Construction of Quantum Gates and Oracles
		22.4 Summary
		Problems
	23 Grover's Algorithm: I
		23.1 Learning Outcomes
		23.2 Grover's Algorithm
			23.2.1 Computational Complexity
			23.2.2 The Problem
			23.2.3 An Overview of Grover's Algorithm
			23.2.4 Implementation of Grover's Algorithm
			23.2.5 Circuit for Grover's Algorithm
		23.3 Summary
		Problems
	24 Grover's Algorithm: II
		24.1 Learning Outcomes
		24.2 Numerical Example for Grover's Algorithm
			24.2.1 Construction of Quantum Oracle
			24.2.2 Construction of the Grover Diffusion Operator
			24.2.3 Evolution of the Wavefunction
		24.3 Simulation on IBM-Q
		24.4 Implementation Using XOR Quantum Oracle
		24.5 Summary
		Problems
	25 Quantum Fourier Transform I
		25.1 Learning Outcomes
		25.2 The N-th Root of Unity
		25.3 Discrete Fourier Transform
		25.4 Quantum Fourier Transform
		25.5 Inverse Quantum Fourier Transform
		25.6 Summary
		Problems
	26 Quantum Fourier Transform II
		26.1 Learning Outcomes
		26.2 Another Definition of QFT and IQFT
		26.3 Many-Qubit SWAP Gate
		26.4 QFT Circuit
			26.4.1 Implementation of a 3-Qubit QFT Circuit
		26.5 Implementation of IQFT
		26.6 General Circuit of QFT
		26.7 Summary
		Problems
	27 Bloch Sphere and Single-Qubit Arbitrary Unitary Gate
		27.1 Learning Outcomes
		27.2 Bloch Sphere
		27.3 Expectation Values of Pauli Matrices
		27.4 Single-Qubit Arbitrary Unitary Rotation
		27.5 Summary
		Problems
	28 Quantum Phase Estimation
		28.1 Learning Outcomes
		28.2 General Controlled Unitary Gate
		28.3 Quantum Phase Estimation
			28.3.1 QPE for a 22 Matrix
			28.3.2 Implementation on IBM-Q
			28.3.3 General QPE Circuit
		28.4 Summary
		Problems
	29 Shor's Algorithm
		29.1 Learning Outcomes
		29.2 Background
			29.2.1 Encryption
			29.2.2 Period Finding
			29.2.3 Prime Integer Factorization
		29.3 Shor's Algorithm
		29.4 Summary
		Problems
	30 The Last But Not the Least
		30.1 Learning Outcomes
		30.2 End of the Beginning
		30.3 Quantum Programming
		30.4 Next Steps
Index