## Quantum ComputingThis introduction to quantum computing presents the most important results obtained thus far in this innovative, multidisciplinary research area which encompasses quantum mechanics, theoretical computer science and mathematics. The material is presented in an accessible manner, uniformly from a computer science viewpoint, which differs from other mainly physics-oriented treatments. Two important algorithms, fast factorization and Grover search, are also discussed in detail. |

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### Contents

Introduction | 1 |

Devices for Computation | 13 |

Fast Factorization | 41 |

Copyright | |

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amplitudes assume binary blackbox function Boolean circuit Boolean functions called classical coefficients completely positive complex numbers compound system configuration convergents coset decomposition defined Definition denoted density matrix eigenvalues eigenvectors element entropy equation evolution Example factor finite Fourier transform give group G Hadamard Hadamard-Walsh Hilbert space inner product input integer inverse isomorphic L(Hn linear mapping matrix multiplication natural numbers notation notion orthogonal orthonormal basis output permutation probabilistic Turing machine probability distribution problem Proof quantum algorithm quantum circuit quantum computation quantum gates quantum mechanics quantum physics quantum system quantum Turing machine qubits queries real number recursively represented resp reversible gates satisfies Section self-adjoint operator simulate sin2 space Hn spectral representation subspace superposition symmetric tensor product Theorem theory Toffoli gate unique unit-length vector unitary mapping variables vector space verify