Quantum computing for everyone

Table of contents

1.Spin
The Quantum Clock
Measurements in the Same Direction
Measurements in Different Directions
Measurements
Randomness
Photons and Polarization
Conclusions
2.Linear Algebra
Complex Numbers versus Real Numbers
Vectors
Diagrams of Vectors
Lengths of Vectors
Scalar Multiplication
Vector Addition
Orthogonal Vectors
Multiplying a Bra by a Ket
Bra-Kets and Lengths
Bra-Kets and Orthogonality
Orthonormal Bases
Vectors as Linear Combinations of Basis Vectors
Ordered Bases
Length of Vectors
Matrices
Matrix Computations
Orthogonal and Unitary Matrices
Linear Algebra Toolbox
3.Spin And Qubits
Probability
Mathematics of Quantum Spin
Equivalent State Vectors
The Basis Associated with a Given Spin Direction
Rotating the Apparatus through 60°
The Mathematical Model for Photon Polarization
The Basis Associated with a Given Polarization Direction
The Polarized Filters Experiments
Qubits
Alice, Bob, and Eve
Probability Amplitudes and Interference
Alice, Bob, Eve, and the BB84 Protocol
4.Entanglement
Alice and Bob's Qubits Are Not Entangled
Unentangled Qubits Calculation
Entangled Qubits Calculation
Superluminal Communication
The Standard Basis for Tensor Products
How Do You Entangle Qubits?
Using the CNOT Gate to Entangle Qubits
Entangled Quantum Clocks
5.Bell's Inequality
Entangled Qubits in Different Bases
Proof That 1/2[10][⊗][10]+1/2[01][⊗][01] Equals 1/2|b0>[⊗]|b0>+1/2|b1>[⊗]|b1>|
Einstein and Local Realism
Einstein and Hidden Variables
A Classical Explanation of Entanglement
Bell's Inequality
The Answer of Quantum Mechanics
The Classical Answer
Measurement
The Ekert Protocol for Quantum Key Distribution
6.Classical Logic, Gates, And Circuits
Logic
Boolean Algebra
Functional Completeness
Gates
Circuits
NAND Is a Universal Gate
Gates and Computation
Memory
Reversible Computation
Billiard Ball Computing
7.Quantum Gates And Circuits
The CNOT Gate
Quantum Gates
Quantum Gates Acting on One Qubit
Are There Universal Quantum Gates?
No Cloning Theorem
Quantum Computation versus Classical Computation
The Bell Circuit
Superdense Coding
Quantum Teleportation
Error Correction
8.Quantum Algorithms
The Complexity Classes P and NP
Are Quantum Algorithms Faster Than Classical Ones?
Query Complexity
Deutsch's Algorithm
The Kronecker Product of Hadamard Matrices
The Deutsch-Jozsa Algorithm
Simon's Algorithm
Complexity Classes
Quantum Algorithms
9.Impact Of Quantum Computing
Shor's Algorithm and Cryptanalysis
Grover's Algorithm and Searching Data
Chemistry and Simulation
Hardware
Quantum Supremacy and Parallel Universes
Computation

An accessible introduction to an exciting new area in computation, explaining such topics as qubits, entanglement, and quantum teleportation for the general reader.
Quantum computing is a beautiful fusion of quantum physics and computer science, incorporating some of the most stunning ideas from twentieth-century physics into an entirely new way of thinking about computation. In this book, Chris Bernhardt offers an introduction to quantum computing that is accessible to anyone who is comfortable with high school mathematics. He explains qubits, entanglement, quantum teleportation, quantum algorithms, and other quantum-related topics as clearly as possible for the general reader. Bernhardt, a mathematician himself, simplifies the mathematics as much as he can and provides elementary examples that illustrate both how the math works and what it means.
Bernhardt introduces the basic unit of quantum computing, the qubit, and explains how the qubit can be measured; discusses entanglement—which, he says, is easier to describe mathematically than verbally—and what it means when two qubits are entangled (citing Einstein's characterization of what happens when the measurement of one entangled qubit affects the second as “spooky action at a distance”); and introduces quantum cryptography. He recaps standard topics in classical computing—bits, gates, and logic—and describes Edward Fredkin's ingenious billiard ball computer. He defines quantum gates, considers the speed of quantum algorithms, and describes the building of quantum computers. By the end of the book, readers understand that quantum computing and classical computing are not two distinct disciplines, and that quantum computing is the fundamental form of computing. The basic unit of computation is the qubit, not the bit.

https://mitpress.mit.edu/books/quantum-computing-everyone