Intro; Contents; Acknowledgments; Introduction; 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 MatricesLinear 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�A; 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 CommunicationThe 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...; 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 GateGates and Computation; Memory; Reversible Computation; Billiard Ball Computing; 7 Quantum Gates and Circuits; Qubits; 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 AlgorithmSimon'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; Index

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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.

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