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Quantum computing : = a gentle introduction /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Quantum computing :/ Eleanor Rieffel and Wolfgang Polak.
Reminder of title:	a gentle introduction /
Author:	Rieffel, Eleanor,
other author:	Polak, Wolfgang,
Published:	Cambridge, Mass. :The MIT Press, : c2011.,
Description:	xiii, 372 p. :ill. ;24 cm.
[NT 15003449]:	Note continued:
Subject:	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 /
LDR:10183cam a2200361 a 4500 001 988425
003 OCoLC
005 20111123060858.0
008 111208s2011 maua b 001 0 eng
010 $a 2010022682
020 $a 9780262015066 (hbk.) : $c US45.00
020 $a 0262015064 (hbk.)
029 1 $a AU@ $b 000045689087
029 1 $a NZ1 $b 13714189
035 $a (OCoLC)641998800
035 $a PS-BW-100-N-07
040 $a DLC $c DLC $d YDX $d YDXCP $d VKC $d BWX $d CDX $d INU $d UKMGB $d IAD $d MIX
049 $a FISA
050 0 0 $a QA76.889 $b .R54 2011
082 0 0 $a 004.1 $2 22
100 1 $a Rieffel, Eleanor, $d 1965- $3 1314434
245 1 0 $a Quantum computing : $b 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