## Quantum Computation and Quantum Information: 10th Anniversary EditionOne of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering. |

### From inside the book

Results 1-5 of 45

Page xi

... quantum Fourier transform 217 5.2 Phase estimation 221 5.2.1 Performance

and requirements 223 5.3 Applications: order-finding and factoring 226 5.3.1

Application: order-finding 226 5.3.2 Application: factoring 232 5.4 General

applications of the quantum Fourier transform 234 5.4.1 Period-finding 236 5.4.2

Discrete logarithms 238 5.4.3 The hidden subgroup problem 240 5.4.4 Other

quantum algorithms? 242 6

... quantum Fourier transform 217 5.2 Phase estimation 221 5.2.1 Performance

and requirements 223 5.3 Applications: order-finding and factoring 226 5.3.1

Application: order-finding 226 5.3.2 Application: factoring 232 5.4 General

applications of the quantum Fourier transform 234 5.4.1 Period-finding 236 5.4.2

Discrete logarithms 238 5.4.3 The hidden subgroup problem 240 5.4.4 Other

quantum algorithms? 242 6

**Quantum search algorithms**248 6.1 The**quantum****search algorithm**... Page xix

Qubits based on nuclear spins and single photons have been used, respectively,

to demonstrate proof-of-principle for simple forms ofquantum error correctionand

quantum simulation. But the most impressive progress of all has been made with

trapped ion systems, which have been used to implement many two- and three-

qubit algorithms and algorithmic building blocks, including the

to ...

Qubits based on nuclear spins and single photons have been used, respectively,

to demonstrate proof-of-principle for simple forms ofquantum error correctionand

quantum simulation. But the most impressive progress of all has been made with

trapped ion systems, which have been used to implement many two- and three-

qubit algorithms and algorithmic building blocks, including the

**quantum search****algorithm**and the quantum Fourier transform. Trapped ions have also been usedto ...

Page xxii

Structure of the book. tal elements needed to perform quantum computation, and

presents many elementary operations which may be used to develop more

sophisticated applications of quantum computation. Chapters 5 and 6 describe

the quantum Fourier transform and the

fundamental quantum algorithms presently known. Chapter 5 also explains how

the quantum Fourier transform may be used to solve the factoring and discrete

logarithm ...

Structure of the book. tal elements needed to perform quantum computation, and

presents many elementary operations which may be used to develop more

sophisticated applications of quantum computation. Chapters 5 and 6 describe

the quantum Fourier transform and the

**quantum search algorithm**, the twofundamental quantum algorithms presently known. Chapter 5 also explains how

the quantum Fourier transform may be used to solve the factoring and discrete

logarithm ...

Page 37

Broadly speaking, there are three classes of quantum algorithms which provide

an advantage over known classical algorithms. First, there is the class of

algorithms based upon quantum versions of the Fourier transform, a tool which is

also widely used in classical algorithms. The Deutsch–Jozsa algorithm is an

example of this type of algorithm, as are Shor's algorithms for factoring and

discrete logarithm. The second class of algorithms is

The third class of ...

Broadly speaking, there are three classes of quantum algorithms which provide

an advantage over known classical algorithms. First, there is the class of

algorithms based upon quantum versions of the Fourier transform, a tool which is

also widely used in classical algorithms. The Deutsch–Jozsa algorithm is an

example of this type of algorithm, as are Shor's algorithms for factoring and

discrete logarithm. The second class of algorithms is

**quantum search algorithms**.The third class of ...

Page 38

represented by the

discovered by Grover. The

problem: Given a search space of size N, and no prior knowledge about the

structure of the information in it, we want to find an element of that search space

satisfying a known property. How long does it take to find an element satisfying

that property? Classically ...

**Quantum search algorithms**A completely different class of algorithms isrepresented by the

**quantum search algorithm**, whose basic principles werediscovered by Grover. The

**quantum search algorithm**solves the followingproblem: Given a search space of size N, and no prior knowledge about the

structure of the information in it, we want to find an element of that search space

satisfying a known property. How long does it take to find an element satisfying

that property? Classically ...

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### Contents

1 | |

Introduction to quantum mechanics | 60 |

Introduction to computer science | 120 |

Quantum computation | 171 |

The quantum Fourier transform and its applications | 216 |

Quantum search algorithms | 248 |

physical realization | 277 |

Quantum information | 353 |

Entropy and information | 500 |

Quantum information theory | 528 |

Appendices | 608 |

The SolovayKitaev theorem | 617 |

Number theory | 625 |

Public key cryptography and the RSA cryptosystem | 640 |

Bibliography | 649 |

Index | 665 |

### Other editions - View all

Quantum Computation and Quantum Information Michael A. Nielsen,Isaac L. Chuang No preview available - 2000 |

Quantum Computation and Quantum Information Michael A. Nielsen,Isaac L. Chuang No preview available - 2000 |

### Common terms and phrases

Alice and Bob ancilla applied arbitrary atom bit ﬂip Bloch sphere chapter classical computer classical information computation and quantum computational basis construction controlled deﬁned deﬁnition density matrix density operator described difﬁcult efﬁciently eigenvalues encoded entanglement entropy equation error error-correcting codes example Exercise factor fault-tolerant ﬁdelity ﬁeld Figure ﬁnal ﬁnd ﬁnite ﬁrst ﬁxed function gives Hadamard gate Hamiltonian implement inequality input integer interaction linear noise obtain operation elements oracle order-ﬁnding orthonormal output Pauli perform phase ﬂip physical polynomial possible POVM probability problem procedure proof properties protocol prove quantum algorithms quantum circuit quantum codes quantum computation quantum error-correction quantum Fourier transform quantum gates quantum information processing quantum mechanics quantum operation quantum search algorithm quantum system result satisﬁes Section Show simulation single qubit solve speciﬁc spin subadditivity sufﬁcient Suppose Toffoli gate trace distance Turing machine unitary matrix unitary operator unitary transform vector space