Atnaujinkite slapukų nuostatas

El. knyga: Amazing World of Quantum Computing

Kitos knygos pagal šią temą:
Amazing World of Quantum ComputingDidesnis paveikslėlis
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

This book discusses the application of quantum mechanics to computing. It explains the fundamental concepts of quantum mechanics and then goes on to discuss various elements of mathematics required for quantum computing. Quantum cryptography, waves and Fourier analysis, measuring quantum systems, comparison to classical mechanics, quantum gates, and important algorithms in quantum computing are among the topics covered.

The book offers a valuable resource for graduate and senior undergraduate students in STEM (science, technology, engineering, and mathematics) fields with an interest in designing quantum algorithms. Readers are expected to have a firm grasp of linear algebra and some familiarity with Fourier analysis. 

1 Quantum Cryptography and Quantum Teleportation
1(16)
1.1 Introduction
1(1)
1.2 Hello to Some Weirdness in Quantum Mechanics
2(2)
1.3 Time for Some Mathematics
4(4)
1.3.1 Quantum Operators that Act on a Qubit
5(2)
1.3.2 A Quantum Operator that Acts on a Qubit Pair
7(1)
1.4 Encryption and Key Distribution
8(3)
1.5 Teleportation
11(3)
1.6 Concluding Remarks
14(1)
References
14(3)
2 Distinguishing Features and Axioms of Quantum Mechanics
17(36)
2.1 Introduction
17(1)
2.2 Two-Layer Description of the World
18(5)
2.2.1 The Observer in Physics
19(1)
2.2.2 Complementarity (Wave-Particle Duality)
19(3)
2.2.3 Causality and Determinism
22(1)
2.3 Superposition, Measurement, and Entanglement
23(2)
2.4 Classical Mechanics Powers Our Intuition
25(1)
2.5 The Birth of Modern Quantum Mechanics
26(4)
2.5.1 Serendipity at Work
28(2)
2.6 Cautionary Note on Notations in Quantum Mechanics
30(1)
2.7 Postulates of Quantum Mechanics Formally Stated
30(7)
2.7.1 A Quantum System's. State Space Is a Hilbert Space
31(1)
2.7.2 A Quantum System Evolves via Unitary Transformations
31(1)
2.7.3 A Quantum System Collapses When Measured
32(1)
2.7.4 Hilbert Space Grows Rapidly with the Size of a Quantum System
33(2)
2.7.5 Bern's Probabilistic Interpretation
35(1)
2.7.6 Heisenberg's Uncertainty Principle
36(1)
2.8 Observables and Operators
37(4)
2.8.1 Observables in Quantum Mechanics Are Operators
38(1)
2.8.2 The Need for Observable-Operators
39(1)
2.8.3 Remarks on Vector Spaces
40(1)
2.9 Weirdness of Quantum Mechanics (In_Summary)
41(2)
2.10 Interpretations of Quantum Mechanics
43(1)
2.10.1 Copenhagen Interpretation
44(1)
2.10.2 Everett's Many-World Interpretation
44(1)
2.10.3 Bohm's Interpretation
45(1)
2.11 From Galileo-Newton to Schrodinger-Born
46(1)
2.12 Concluding Remarks
47(1)
References
48(5)
3 Mathematical Elements Needed to Compute
53(24)
3.1 Introduction
53(3)
3.1.1 Prepositional Calculus (Prepositional Logic)
54(1)
3.1.2 First-Order Predicate Calculus (First Order Logic)
55(1)
3.2 Elements of Linear Algebra
56(5)
3.2.1 Various Representations of a State Vector
56(2)
3.2.2 Bases and Linear Independence
58(3)
3.3 Linear Operators and Matrices
61(1)
3.3.1 Inner Product
62(1)
3.3.2 Outer Product
63(1)
3.3.3 Tensor Product
64(3)
3.4 Eigenvalue, Eigenvector, Spectral Decomposition, Trace
67(5)
3.4.1 Eigenvalues and Eigenvectors
67(1)
3.4.2 Diagonal Representation of an Operator or Orthonormal Decomposition
68(1)
3.4.3 Normal Operators and Spectral Decomposition
68(1)
3.4.4 Unitary Operators
69(1)
3.4.5 Positive Operator
70(1)
3.4.6 Trace of a Matrix
70(1)
3.4.7 Commutator and Anti-Commutator
71(1)
3.4.8 Polar and Singular Value Decompositions
71(1)
3.4.9 Completeness Relation
72(1)
3.5 Cauchy-Schwarz Inequality
72(1)
3.6 Pauli Matrices
73(1)
3.7 Concluding Remarks
74(1)
References
75(2)
4 Some Mathematical Consequences of the Postulates
77(22)
4.1 Introduction
77(1)
4.2 No-Cloning Theorem
78(2)
4.2.1 Consequences of the No-Cloning Theorem
80(1)
4.3 No-Deleting Theorem
80(1)
4.4 No-Hiding Theorem
81(1)
4.5 EPR Paradox and Bell Inequalities
82(8)
4.5.1 An Analogy for Factorizable States
83(1)
4.5.2 Einstein, Podolsky, Rosen Pose a Paradox
83(2)
4.5.3 What Does Hidden Variable Theory Mean?
85(1)
4.5.4 Bell Inequality
86(2)
4.5.5 An Intriguing Question
88(1)
4.5.6 Returning to the Bell Inequality
89(1)
4.5.7 Would Newton Have Approved of Entanglement?
90(1)
4.6 Superposition and Indeterminacy
90(1)
4.7 Mathematical Consequences
91(3)
4.8 Concluding Remarks
94(1)
References
95(4)
5 Waves and Fourier Analyses
99(12)
5.1 Introduction
99(1)
5.2 Waves
99(7)
5.2.1 The Wave Equation
103(1)
5.2.2 Travelling Waves
103(1)
5.2.3 Standing or Stationary Waves
103(1)
5.2.4 Wave Packets
104(1)
5.2.5 Probability Waves
105(1)
5.3 Fourier Analysis
106(1)
5.4 Wave Packets in Some Detail
107(2)
5.4.1 Group and Phase Velocities
108(1)
5.5 Concluding Remarks
109(1)
References
109(2)
6 Getting a Hang of Measurement
111(18)
6.1 Introduction
111(1)
6.2 Measurement of Quantum Systems
112(11)
6.2.1 Cascaded Measurements Are Single Measurements
114(1)
6.2.2 Projective Measurements; Observable-Operators
115(3)
6.2.3 Distinguishing Quantum States
118(1)
6.2.4 When Measurement Basis States Differ from Computational Basis States
118(1)
6.2.5 Positive Operator-Valued Measure (POVM) Measurements
119(1)
6.2.6 The Effect of Phase on Measurement
120(1)
6.2.7 Can Every Observable Be Measured?
121(1)
6.2.8 Measurement with Photons and Electrons
121(1)
6.2.9 Whither Causality?
122(1)
6.3 Heisenberg's Uncertainty Principle (Revisited)
123(3)
6.4 Concluding Remarks
126(1)
References
127(2)
7 Quantum Gates
129(26)
7.1 Introduction
129(2)
7.2 Operators (A Summary)
131(1)
7.3 The Qubit
132(4)
7.3.1 Global Phase Factor
134(1)
7.3.2 Relative Phase Factor
134(1)
7.3.3 Unitary Operators
134(2)
7.3.4 Hermitian Operators
136(1)
7.4 Important Qubit Gates
136(9)
7.4.1 Pauli Gates and Other 1-Qubit Gates
136(2)
7.4.2 2-Qubit Controlled-not Gate
138(2)
7.4.3 Creating Entangled Bell States
140(1)
7.4.4 Bit Copying--An Application of the Controlled-not Gate
141(1)
7.4.5 3-Qubit Toffoli Gate
141(2)
7.4.6 3-Bit Fredkin Gate
143(1)
7.4.7 Controlled-U Gate
144(1)
7.5 Universal Set of Gates
145(3)
7.5.1 Universal Set of Classical Gates
145(1)
7.5.2 Universal Set of Quantum Gates
146(2)
7.6 Some Basic Quantum Operations
148(1)
7.6.1 Random Number Generation
148(1)
7.6.2 n-Qubit Hadamard Gate
148(1)
7.6.3 A 3-Qubit Gate for AND and NOT Operations
149(1)
7.7 Taking Stock of Gates
149(3)
7.8 Concluding Remarks
152(1)
References
153(2)
8 Unusual Solutions of Usual Problems
155(16)
8.1 Introduction
155(3)
8.1.1 Mach-Zehnder Interferometer
156(2)
8.2 Some Simple Quantum Algorithms
158(11)
8.2.1 Computing x Ay
158(1)
8.2.2 Computing x + y
159(1)
8.2.3 Swapping States
159(1)
8.2.4 The Deutsch Algorithm
160(2)
8.2.5 The Deutsch-Jozsa Algorithm
162(1)
8.2.6 Computing J(x) in Parallel
163(1)
8.2.7 Hardy's Reprieve
164(2)
8.2.8 The Elitzur-Vaidman Bomb Problem
166(2)
8.2.9 Securing Banknotes
168(1)
8.3 Concluding Remarks
169(1)
References
169(2)
9 Fundamental Limits to Computing
171(36)
9.1 Introduction
171(1)
9.2 Hilbert's Second Problem
172(3)
9.2.1 Recursive Set
174(1)
9.3 Hilbert's Tenth Problem
175(2)
9.4 Turing and the Entscheidungsproblem
177(8)
9.4.1 Turing's Halting Problem
179(4)
9.4.2 The Church-Turing Thesis
183(1)
9.4.3 Deutsch on the Church-Turing Thesis
184(1)
9.4.4 Can Quantum Computers Prove Theorems?
185(1)
9.5 Thermodynamic Considerations
185(10)
9.5.1 The One-Molecule Gas
187(1)
9.5.2 Knowledge and Entropy
188(1)
9.5.3 Information Is Physical
188(2)
9.5.4 Toffoli Gate
190(1)
9.5.5 Bennett's Solution for Junk Bits
191(1)
9.5.6 Reversible Classical Computation Set the Stage for Quantum Computing
192(1)
9.5.7 Maxwell's Demon
192(3)
9.6 Computational Complexity
195(8)
9.6.1 Classification of Complexity
199(4)
9.6.2 NP-Complete Problems Stand or Fall Together
203(1)
9.7 Concluding Remarks
203(1)
References
204(3)
10 The Crown Jewels of Quantum Algorithms
207(34)
10.1 Introduction
207(1)
10.2 General Remarks on Quantum Algorithms
208(1)
10.3 Modulo Arithmetic
209(2)
10.3.1 Some Important Properties of Congruence
209(1)
10.3.2 Congruence "Classes"
210(1)
10.3.3 Modulo 2 Arithmetic
211(1)
10.4 Bits and Qubits
211(3)
10.4.1 Bitwise Operators
212(1)
10.4.2 String Manipulation Leads to Algorithms
212(2)
10.5 UTM, DTM, FTM, and QTM
214(2)
10.5.1 Are Quantum Computers More Powerful?
215(1)
10.6 The Quantum Fourier Transform
216(5)
10.6.1 Background
216(1)
10.6.2 Quantum Fourier Transform
217(4)
10.7 Computing the Period of a Sequence
221(3)
10.8 Shor's Factoring Algorithm
224(3)
10.8.1 Shor's Algorithm" Implemented
226(1)
10.8.2 Computational Complexity of Shor's Algorithm
226(1)
10.9 Phase Estimation Problem
227(2)
10.10 Graver's Search Algorithm
229(5)
10.10.1 Graver's Algorithm Verified
233(1)
10.10.2 Computational Complexity of Graver's Algorithm
234(1)
10.10.3 Remarks on Graver's Algorithm
234(1)
10.11 Dense Coding and Teleportation
234(3)
10.11.1 Dense Coding
235(1)
10.11.2 Teleportation
236(1)
10.12 Concluding Remarks
237(1)
References
238(3)
11 Quantum Error Corrections
241(12)
11.1 Introduction
241(1)
11.2 Protecting the Computational Hilbert Space
242(4)
11.2.1 Dissipation
243(1)
11.2.2 Decoherence
244(2)
11.2.3 Algorithmic Error Correction Is Possible
246(1)
11.3 Calderbank-Shor-Steane Error Correction
246(4)
11.3.1 Encoding-Decoding
246(1)
11.3.2 Steps of Error Correction
247(3)
11.4 Decoherence-Free Subspace
250(1)
11.5 Concluding Remarks
251(1)
References
251(2)
12 Time-Multiplexed Interpretation of Measurement
253(10)
12.1 Introduction
253(2)
12.2 A Conjectured Sub-planck Mechanism
255(3)
12.3 Application of the Basic Model
258(1)
12.3.1 Measurement of a Two-Particle Entangled System
258(1)
12.3.2 Quantum Adder
259(1)
12.4 Teleporting a Qubit of an Unknown State
259(3)
12.5 Concluding Remarks
262(1)
References
262(1)
Index 263
Rajendra Bera, Ph.D., is Chief Mentor at Acadinnet Education Services, Bengaluru, India since 2010. He received his B.Tech., M.Tech., and Ph.D. degrees in Aeronautical Engineering from the Indian Institute of Technology Kanpur, India. From 1979 to 1980, he was Visiting Assistant Professor of Aerospace, Mechanical, and Nuclear Engineering at the University of Oklahoma, USA, and in 1988 Visiting Faculty of Aerospace Engineering at the Indian Institute of Technology Kanpur, India, where he taught the fighter aircraft design. From 2006 to 2011, he was Honorary Professor at the International Institute of Information Technology, Bengaluru, India, where he taught quantum computing and intellectual property rights. From 2013-2014, he was a Visiting Professor at the Department of Aerospace Engineering, Jain University, Bengaluru, India, where he taught the fighter aircraft design and intellectual property rights. During his student days, he was an active amateur pilot.

From 1971 to 1995, Dr. Bera served at the National Aerospace Laboratories, Bangalore, where he worked in aerodynamics, flight dynamics, theory of elasticity, neural networks, science and technology policy, and technology transfer to industry. From 1995 to 2005, he worked at IBM Software Labs, Bangalore, where he developed an R&D group focusing on new technologies and mentored young researchers and inventors. He is the sole inventor on 28 US patents, all assigned to IBM. His patenting areas include compiler optimization, resource allocation, pattern recognition, and static analysis of computer codes. A former member of the New York Academy of Sciences, Dr. Bera is a fellow of the Institution of Engineers (India) and is listed in several editions of Marquis Whos Who. The sole author of more than 40 research publications in prominent journals, his current research interests include pattern recognition in molecular biology, quantum computing, intellectual property rights, and nonlinear dynamical systems.
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97898115247146e.html
Raktažodžiai: