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Quantum computing : = a gentle intro...
~
Rieffel, Eleanor, (1965-)
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Quantum computing : = a gentle introduction /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Quantum computing :/ Eleanor Rieffel and Wolfgang Polak.
其他題名:
a gentle introduction /
作者:
Rieffel, Eleanor,
其他作者:
Polak, Wolfgang,
出版者:
Cambridge, Mass. :The MIT Press, : c2011.,
面頁冊數:
xiii, 372 p. :ill. ;24 cm.
內容註:
Note continued:
標題:
Quantum computers. -
ISBN:
9780262015066 (hbk.) :
Quantum computing : = a gentle introduction /
Rieffel, Eleanor,1965-
Quantum computing :
a gentle introduction /Eleanor Rieffel and Wolfgang Polak. - Cambridge, Mass. :The MIT Press,c2011. - xiii, 372 p. :ill. ;24 cm. - Scientific and engineering computation. - Scientific and engineering computation..
Includes bibliographical references and index.
Introduction --Machine generated contents note:
ISBN: 9780262015066 (hbk.) :US45.00
LCCN: 2010022682Subjects--Topical Terms:
535318
Quantum computers.
LC Class. No.: QA76.889 / .R54 2011
Dewey Class. No.: 004.1
Quantum computing : = a gentle introduction /
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Quantum computing :
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a gentle introduction /
$c
Eleanor Rieffel and Wolfgang Polak.
260
$a
Cambridge, Mass. :
$b
The MIT Press,
$c
c2011.
300
$a
xiii, 372 p. :
$b
ill. ;
$c
24 cm.
490
1
$a
Scientific and engineering computation
504
$a
Includes bibliographical references and index.
505
0 0
$g
Machine generated contents note:
$g
1.
$t
Introduction --
$g
I.
$t
QUANTUM BUILDING BLOCKS --
$g
2.
$t
Single-Qubit Quantum Systems --
$g
2.1.
$t
The Quantum Mechanics of Photon Polarization --
$g
2.1.1.
$t
A Simple Experiment --
$g
2.1.2.
$t
A Quantum Explanation --
$g
2.2.
$t
Single Quantum Bits --
$g
2.3.
$t
Single-Qubit Measurement --
$g
2.4.
$t
A Quantum Key Distribution Protocol --
$g
2.5.
$t
The State Space of a Single-Qubit System --
$g
2.5.1.
$t
Relative Phases versus Global Phases --
$g
2.5.2.
$t
Geometric Views of the State Space of a Single Qubit --
$g
2.5.3.
$t
Comments on General Quantum State Spaces --
$g
2.6.
$t
References --
$g
2.7.
$t
Exercises --
$g
3.
$t
Multiple-Qubit Systems --
$g
3.1.
$t
Quantum State Spaces --
$g
3.1.1.
$t
Direct Sums of Vector Spaces --
$g
3.1.2.
$t
Tensor Products of Vector Spaces --
$g
3.1.3.
$t
The State Space of an n-Qubit System --
$g
3.2.
$t
Entangled States --
$g
3.3.
$t
Basics of Multi-Qubit Measurement --
$g
3.4.
$t
Quantum Key Distribution Using Entangled States --
$g
3.5.
$t
References --
$g
3.6.
$t
Exercises --
$g
4.
$t
Measurement of Multiple-Qubit States --
$g
4.1.
$t
Dirac's Bra/Ket Notation for Linear Transformations
505
0 0
$g
4.2.
$t
Projection Operators for Measurement --
$g
4.3.
$t
Hermitian Operator Formalism for Measurement --
$g
4.3.1.
$t
The Measurement Postulate --
$g
4.4.
$t
EPR Paradox and Bell's Theorem --
$g
4.4.1.
$t
Setup for Bell's Theorem --
$g
4.4.2.
$t
What Quantum Mechanics Predicts --
$g
4.4.3.
$t
Special Case of Bell's Theorem: What Any Local Hidden Variable Theory Predicts --
$g
4.4.4.
$t
Bell's Inequality --
$g
4.5.
$t
References --
$g
4.6.
$t
Exercises --
$g
5.
$t
Quantum State Transformations --
$g
5.1.
$t
Unitary Transformations --
$g
5.1.1.
$t
Impossible Transformations: The No-Cloning Principle --
$g
5.2.
$t
Some Simple Quantum Gates --
$g
5.2.1.
$t
The Pauli Transformations --
$g
5.2.2.
$t
The Hadamard Transformation --
$g
5.2.3.
$t
Multiple-Qubit Transformations from Single-Qubit Transformations --
$g
5.2.4.
$t
The Controlled-not and Other Singly Controlled Gates --
$g
5.3.
$t
Applications of Simple Gates --
$g
5.3.1.
$t
Dense Coding --
$g
5.3.2.
$t
Quantum Teleportation --
$g
5.4.
$t
Realizing Unitary Transformations as Quantum Circuits --
$g
5.4.1.
$t
Decomposition of Single-Qubit Transformations --
$g
5.4.2.
$t
Singly-Controlled Single-Qubit Transformations --
$g
5.4.3.
$t
Multiply-Controlled Single-Qubit Transformations
505
0 0
$g
5.4.4.
$t
General Unitary Transformations --
$g
5.5.
$t
A Universally Approximating Set of Gates --
$g
5.6.
$t
The Standard Circuit Model --
$g
5.7.
$t
References --
$g
5.8.
$t
Exercises --
$g
6.
$t
Quantum Versions of Classical Computations --
$g
6.1.
$t
From Reversible Classical Computations to Quantum Computations --
$g
6.1.1.
$t
Reversible and Quantum Versions of Simple Classical Gates --
$g
6.2.
$t
Reversible Implementations of Classical Circuits --
$g
6.2.1.
$t
A Naive Reversible Implementation --
$g
6.2.2.
$t
A General Construction --
$g
6.3.
$t
A Language for Quantum Implementations --
$g
6.3.1.
$t
The Basics --
$g
6.3.2.
$t
Functions --
$g
6.4.
$t
Some Example Programs for Arithmetic Operations --
$g
6.4.1.
$t
Efficient Implementation of and --
$g
6.4.2.
$t
Efficient Implementation of Multiply-Controlled Single-Qubit Transformations --
$g
6.4.3.
$t
In-Place Addition --
$g
6.4.4.
$t
Modular Addition --
$g
6.4.5.
$t
Modular Multiplication --
$g
6.4.6.
$t
Modular Exponentiation --
$g
6.5.
$t
References --
$g
6.6.
$t
Exercises --
$g
II.
$t
QUANTUM ALGORITHMS --
$g
7.
$t
Introduction to Quantum Algorithms --
$g
7.1.
$t
Computing with Superpositions --
$g
7.1.1.
$t
The Walsh-Hadamard Transformation
505
0 0
$g
7.1.2.
$t
Quantum Parallelism --
$g
7.2.
$t
Notions of Complexity --
$g
7.2.1.
$t
Query Complexity --
$g
7.2.2.
$t
Communication Complexity --
$g
7.3.
$t
A Simple Quantum Algorithm --
$g
7.3.1.
$t
Deutsch's Problem --
$g
7.4.
$t
Quantum Subroutines --
$g
7.4.1.
$t
The Importance of Unentangling Temporary Qubits in Quantum Subroutines --
$g
7.4.2.
$t
Phase Change for a Subset of Basis Vectors --
$g
7.4.3.
$t
State-Dependent Phase Shifts --
$g
7.4.4.
$t
State-Dependent Single-Qubit Amplitude Shifts --
$g
7.5.
$t
A Few Simple Quantum Algorithms --
$g
7.5.1.
$t
Deutsch-Jozsa Problem --
$g
7.5.2.
$t
Bernstein-Vazirani Problem --
$g
7.5.3.
$t
Simon's Problem --
$g
7.5.4.
$t
Distributed Computation --
$g
7.6.
$t
Comments on Quantum Parallelism --
$g
7.7.
$t
Machine Models and Complexity Classes --
$g
7.7.1.
$t
Complexity Classes --
$g
7.7.2.
$t
Complexity: Known Results --
$g
7.8.
$t
Quantum Fourier Transformations --
$g
7.8.1.
$t
The Classical Fourier Transform --
$g
7.8.2.
$t
The Quantum Fourier Transform --
$g
7.8.3.
$t
A Quantum Circuit for Fast Fourier Transform --
$g
7.9.
$t
References --
$g
7.10.
$t
Exercises --
$g
8.
$t
Shor's Algorithm --
$g
8.1.
$t
Classical Reduction to Period-Finding
505
0 0
$g
8.2.
$t
Shor's Factoring Algorithm --
$g
8.2.1.
$t
The Quantum Core --
$g
8.2.2.
$t
Classical Extraction of the Period from the Measured Value --
$g
8.3.
$t
Example Illustrating Shor's Algorithm --
$g
8.4.
$t
The Efficiency of Shor's Algorithm --
$g
8.5.
$t
Omitting the Internal Measurement --
$g
8.6.
$t
Generalizations --
$g
8.6.1.
$t
The Discrete Logarithm Problem --
$g
8.6.2.
$t
Hidden Subgroup Problems --
$g
8.7.
$t
References --
$g
8.8.
$t
Exercises --
$g
9.
$t
Graver's Algorithm and Generalizations --
$g
9.1.
$t
Graver's Algorithm --
$g
9.1.1.
$t
Outline --
$g
9.1.2.
$t
Setup --
$g
9.1.3.
$t
The Iteration Step --
$g
9.1.4.
$t
How Many Iterations? --
$g
9.2.
$t
Amplitude Amplification --
$g
9.2.1.
$t
The Geometry of Amplitude Amplification --
$g
9.3.
$t
Optimality of Grover's Algorithm --
$g
9.3.1.
$t
Reduction to Three Inequalities --
$g
9.3.2.
$t
Proofs of the Three Inequalities --
$g
9.4.
$t
Derandomization of Grover's Algorithm and Amplitude Amplification --
$g
9.4.1.
$t
Approach 1: Modifying Each Step --
$g
9.4.2.
$t
Approach 2: Modifying Only the Last Step --
$g
9.5.
$t
Unknown Number of Solutions --
$g
9.5.1.
$t
Varying the Number of Iterations --
$g
9.5.2.
$t
Quantum Counting
505
0 0
$g
9.6.
$t
Practical Implications of Grover's Algorithm and Amplitude Amplification --
$g
9.7.
$t
References --
$g
9.8.
$t
Exercises --
$g
III.
$t
ENTANGLED SUBSYSTEMS AND ROBUST QUANTUM COMPUTATION --
$g
10.
$t
Quantum Subsystems and Properties of Entangled States --
$g
10.1.
$t
Quantum Subsystems and Mixed States --
$g
10.1.1.
$t
Density Operators --
$g
10.1.2.
$t
Properties of Density Operators --
$g
10.1.3.
$t
The Geometry of Single-Qubit Mixed States --
$g
10.1.4.
$t
Von Neumann Entropy --
$g
10.2.
$t
Classifying Entangled States --
$g
10.2.1.
$t
Bipartite Quantum Systems --
$g
10.2.2.
$t
Classifying Bipartite Pure States up to LOCC Equivalence --
$g
10.2.3.
$t
Quantifying Entanglement in Bipartite Mixed States --
$g
10.2.4.
$t
Multipartite Entanglement --
$g
10.3.
$t
Density Operator Formalism for Measurement --
$g
10.3.1.
$t
Measurement of Density Operators --
$g
10.4.
$t
Transformations of Quantum Subsystems and Decoherence --
$g
10.4.1.
$t
Superoperators --
$g
10.4.2.
$t
Operator Sum Decomposition --
$g
10.4.3.
$t
A Relation Between Quantum State Transformations and Measurements --
$g
10.4.4.
$t
Decoherence --
$g
10.5.
$t
References --
$g
10.6.
$t
Exercises --
$g
11.
$t
Quantum Error Correction
505
0 0
$g
11.1.
$t
Three Simple Examples of Quantum Error Correcting Codes --
$g
11.1.1.
$t
A Quantum Code That Corrects Single Bit-Flip Errors --
$g
11.1.2.
$t
A Code for Single-Qubit Phase-Flip Errors --
$g
11.1.3.
$t
A Code for All Single-Qubit Errors --
$g
11.2.
$t
Framework for Quantum Error Correcting Codes --
$g
11.2.1.
$t
Classical Error Correcting Codes --
$g
11.2.2.
$t
Quantum Error Correcting Codes --
$g
11.2.3.
$t
Correctable Sets of Errors for Classical Codes --
$g
11.2.4.
$t
Correctable Sets of Errors for Quantum Codes --
$g
11.2.5.
$t
Correcting Errors Using Classical Codes --
$g
11.2.6.
$t
Diagnosing and Correcting Errors Using Quantum Codes --
$g
11.2.7.
$t
Quantum Error Correction across Multiple Blocks --
$g
11.2.8.
$t
Computing on Encoded Quantum States --
$g
11.2.9.
$t
Superpositions and Mixtures of Correctable Errors Are Correctable --
$g
11.2.10.
$t
The Classical Independent Error Model --
$g
11.2.11.
$t
Quantum Independent Error Models --
$g
11.3.
$t
CSS Codes --
$g
11.3.1.
$t
Dual Classical Codes --
$g
11.3.2.
$t
Construction of CSS Codes from Classical Codes Satisfying a Duality Condition --
$g
11.3.3.
$t
The Steane Code --
$g
11.4.
$t
Stabilizer Codes
505
0 0
$g
13.4.
$t
Alternatives to the Circuit Model of Quantum Computation --
$g
13.4.1.
$t
Measurement-Based Cluster State Quantum Computation --
$g
13.4.2.
$t
Adiabatic Quantum Computation --
$g
13.4.3.
$t
Holonomic Quantum Computation --
$g
13.4.4.
$t
Topological Quantum Computation --
$g
13.5.
$t
Quantum Protocols --
$g
13.6.
$t
Insight into Classical Computation --
$g
13.7.
$t
Building Quantum Computers --
$g
13.8.
$t
Simulating Quantum Systems --
$g
13.9.
$t
Where Does the Power of Quantum Computation Come From? --
$g
13.10.
$t
What if Quantum Mechanics Is Not Quite Correct? --
$t
APPENDIXES --
$g
A.
$t
Some Relations Between Quantum Mechanics and Probability Theory --
$g
A.1.
$t
Tensor Products in Probability Theory --
$g
A.2.
$t
Quantum Mechanics as a Generalization of Probability Theory --
$g
A.3.
$t
References --
$g
A.4.
$t
Exercises --
$g
B.
$t
Solving the Abelian Hidden Subgroup Problem
505
0 0
$a
Note continued:
$g
B.1.
$t
Representations of Finite Abelian Groups --
$g
B.1.1.
$t
Schur's Lemma --
$g
B.2.
$t
Quantum Fourier Transforms for Finite Abelian Groups --
$g
B.2.1.
$t
The Fourier Basis of an Abelian Group --
$g
B.2.2.
$t
The Quantum Fourier Transform Over a Finite Abelian Group --
$g
B.3.
$t
General Solution to the Finite Abelian Hidden Subgroup Problem --
$g
B.4.
$t
Instances of the Abelian Hidden Subgroup Problem --
$g
B.4.1.
$t
Simon's Problem --
$g
B.4.2.
$t
Shor's Algorithm: Finding the Period of a Function --
$g
B.5.
$t
Comments on the Non-Abelian Hidden Subgroup Problem --
$g
B.6.
$t
References --
$g
B.7.
$t
Exercises.
650
0
$a
Quantum computers.
$3
535318
650
0
$a
Quantum theory.
$3
516552
700
1
$a
Polak, Wolfgang,
$d
1950-
$3
1314435
830
0
$a
Scientific and engineering computation.
$3
808863
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