## An Introduction to Quantum ComputingThis concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However,prior familiarity with topics such as quantum mechanics and computational complexity is not required. |

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### Contents

1 INTRODUCTION AND BACKGROUND | 1 |

2 LINEAR ALGEBRA AND THE DIRAC NOTATION | 21 |

3 QUBITS AND THE FRAMEWORK OF QUANTUM MECHANICS | 38 |

4 A QUANTUM MODEL OF COMPUTATION | 61 |

5 SUPERDENSE CODING AND QUANTUM TELEPORTATION | 78 |

6 INTRODUCTORY QUANTUM ALGORITHMS | 86 |

7 ALGORITHMS WITH SUPERPOLYNOMIAL SPEEDUP | 110 |

8 ALGORITHMS BASED ON AMPLITUDE AMPLIFICATION | 152 |

9 QUANTUM COMPUTATIONAL COMPLEXITY THEORY AND LOWER BOUNDS | 179 |

10 QUANTUM ERROR CORRECTION | 204 |

APPENDIX A | 241 |

260 | |

270 | |

### Other editions - View all

An Introduction to Quantum Computing Phillip Kaye,Raymond Laflamme,Michele Mosca Limited preview - 2006 |

An Introduction to Quantum Computing Phillip Kaye,Raymond Laflamme,Michele Mosca No preview available - 2006 |

### Common terms and phrases

1-qubit gates amplitude ancilla apply bit flip black-box Bloch sphere Church–Turing Thesis classical algorithm classical computer cnot gate codeword computational basis consider control qubit corresponding defined denote density operator described Dirac notation discrete logarithm efficiently eigenvalue eigenvalue estimation eigenvectors encoding Equation equivalent error correction error model error operators example Exercise factor fault-tolerant finite function f Hadamard gate hidden subgroup Hilbert space illustrated in Figure implement input integer linear lower bound maps Neumann measurement Note order-finding orthogonal output parity phase flip photon polynomial probabilistic Turing machine probability at least quantum algorithm quantum circuit quantum computing quantum mechanics quantum searching qubit query complexity real numbers recovery operation second register Section shown in Figure simulate solution solve string subspace superposition Suppose tensor product Theorem three-bit code three-qubit Toffoli gate transformation uniformly at random unitary operator vector space wires