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Quantum computing : a gentle introduction /
A thorough exposition of quantum computing and the underlying concepts of quantum physics, with explanations of the relevant mathematics and numerous examples.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, Mass. :
MIT Press,
2011.
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| Colección: | Scientific and engineering computation.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Rieffel, Eleanor, |d 1965- |1 https://id.oclc.org/worldcat/entity/E39PBJxWWM8Hykr4GrVpbdBMfq | |
| 245 | 1 | 0 | |a Quantum computing : |b a gentle introduction / |c Eleanor Rieffel and Wolfgang Polak. |
| 260 | |a Cambridge, Mass. : |b MIT Press, |c 2011. | ||
| 300 | |a 1 online resource (xiii, 372 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Scientific and engineering computation | |
| 504 | |a Includes bibliographical references and indexes. | ||
| 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 | |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. |
| 588 | 0 | |a Print version record. | |
| 520 | |a A thorough exposition of quantum computing and the underlying concepts of quantum physics, with explanations of the relevant mathematics and numerous examples. | ||
| 546 | |a English. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Quantum computers. | |
| 650 | 0 | |a Quantum theory. | |
| 650 | 2 | |a Quantum Theory | |
| 650 | 6 | |a Ordinateurs quantiques. | |
| 650 | 6 | |a Théorie quantique. | |
| 650 | 7 | |a COMPUTERS |x Hardware |x Mainframes & Minicomputers. |2 bisacsh | |
| 650 | 7 | |a Quantum computers |2 fast | |
| 650 | 7 | |a Quantum theory |2 fast | |
| 650 | 7 | |a Kvantdatorer. |2 sao | |
| 650 | 7 | |a Kvantteori. |2 sao | |
| 700 | 1 | |a Polak, Wolfgang, |d 1950- |1 https://id.oclc.org/worldcat/entity/E39PCjBQcQmqHRj8ktkPkkgqPP | |
| 758 | |i has work: |a Quantum computing (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGm6yhc4t3PPHWmqmV9TBP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Rieffel, Eleanor, 1965- |t Quantum computing. |d Cambridge, Mass. : MIT Press, 2011 |z 9780262015066 |z 0262015064 |w (DLC) 2010022682 |w (OCoLC)641998800 |
| 830 | 0 | |a Scientific and engineering computation. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3339229 |z Texto completo |
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