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E-grāmata: Principles Of Quantum Computation And Information: A Comprehensive Textbook

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(Univ Degli Studi Dell' Insubria, Italy & Instituto Nazionale Per La Fisica Della Materia, Italy), , (Univ Degli Studi Dell' Insubria, Italy & Instituto Nazionale Per La Fisica Della Materia, Italy), (Scuola Normale Superiore, Italy)
  • Formāts: 704 pages
  • Izdošanas datums: 12-Dec-2018
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813237247
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Principles Of Quantum Computation And Information: A Comprehensive TextbookPalielināt
  • Formāts: 704 pages
  • Izdošanas datums: 12-Dec-2018
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789813237247
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'The book is a useful compendium of most significant topics in quantum information and computation It is readable by any undergraduate or graduate student in physics, mathematics, computer science, chemistry or engineering The book has a simple, attractive, easy to grasp and systematic treatment, with the final goal to be used as a substantial wide-ranging primer and single comprehensive material for quantum computation and information without the need for consulting supplementary texts.'Contemporary PhysicsQuantum computation and information is a rapidly developing interdisciplinary field. It is not easy to understand its fundamental concepts and central results without facing numerous technical details. This book provides the reader with a useful guide. In particular, the initial chapters offer a simple and self-contained introduction; no previous knowledge of quantum mechanics or classical computation is required.Various important aspects of quantum computation and information are covered in depth, starting from the foundations (the basic concepts of computational complexity, energy, entropy, and information, quantum superposition and entanglement, elementary quantum gates, the main quantum algorithms, quantum teleportation, and quantum cryptography) up to advanced topics (like entanglement measures, quantum discord, quantum noise, quantum channels, quantum error correction, quantum simulators and tensor networks).It can be used as a broad range textbook for a course in quantum information and computation, both for upper-level undergraduate students and for graduate students. It contains a large number of solved exercises, which are an essential complement to the text, as they will help the student to become familiar with the subject. The book may also be useful as general education for readers who want to know the fundamental principles of quantum information and computation and who have the basic background acquired from their undergraduate course in physics, mathematics, or computer science, as well as for researchers interested in some of the latest spin-off of the field, including the use of quantum information in the theories of many-body systems.
Preface vii
Introduction 1(8)
1 Introduction to classical computation 9(46)
1.1 The Turing machine
9(7)
1.1.1 Addition on a Turing machine
11(2)
1.1.2 The Church-Turing thesis
13(1)
1.1.3 The universal Turing machine
14(1)
1.1.4 The probabilistic Turing machine
15(1)
1.1.5 * The halting problem
15(1)
1.2 The circuit model of computation
16(6)
1.2.1 Binary arithmetics
17(1)
1.2.2 Elementary logic gates
18(3)
1.2.3 Universal classical computation
21(1)
1.3 Computational complexity
22(12)
1.3.1 Tractable vs. intractable problems
23(7)
1.3.2 Complexity classes
30(4)
1.3.3 * The Chernoff bound
34(1)
1.4 * Computing dynamical systems
34(5)
1.4.1 * Deterministic chaos
35(2)
1.4.2 * Algorithmic complexity
37(2)
1.5 Energy and information
39(4)
1.5.1 Maxwell's demon
39(1)
1.5.2 Landauer's principle
40(2)
1.5.3 Extracting work from information
42(1)
1.6 Reversible computation
43(5)
1.6.1 Toffoli and Fredkin gates
45(1)
1.6.2 * The billiard-ball computer
46(2)
1.7 * Energy dissipation in computation
48(6)
1.7.1 * Experimental realization of a Maxwell's demon
48(1)
1.7.2 * Experimental verification of Landauer's principle
49(1)
1.7.3 * Energy dissipation in real classical computer
50(1)
1.7.4 * Experimental realization of reversible computers
51(2)
1.7.5 * Neuromorfic computing
53(1)
1.8 A guide to the bibliography
54(1)
2 Introduction to quantum mechanics 55(42)
2.1 The Stern-Gerlach experiment
56(3)
2.2 Young's double-slit experiment
59(4)
2.3 The postulates of quantum mechanics
63(9)
2.3.1 Dynamical evolution
63(1)
2.3.2 Outcomes of a measurement
64(3)
2.3.3 The post-measurement state
67(2)
2.3.4 Heisenberg's uncertainty principle
69(3)
2.4 The EPR paradox
72(5)
2.5 Bell's inequalities
77(4)
2.6 The density matrix
81(8)
2.6.1 Composite systems
86(3)
2.7 The Schmidt decomposition
89(2)
2.8 Purification
91(2)
2.9 Generalized measurements
93(3)
2.9.1 POVM measurements
94(2)
2.10 A guide to the bibliography
96(1)
3 Quantum computation 97(60)
3.1 The qubit
98(5)
3.1.1 Pure qubit states: The Bloch sphere
99(1)
3.1.2 Mixed qubit states: The Bloch ball
100(3)
3.2 Measuring the state of a qubit
103(2)
3.2.1 Pure qubit states
103(1)
3.2.2 Mixed qubit states
104(1)
3.3 The circuit model of quantum computation
105(3)
3.4 Single-qubit gates
108(3)
3.4.1 Rotations of the Bloch sphere
109(2)
3.5 Controlled gates and entanglement generation
111(5)
3.5.1 The Bell basis
115(1)
3.6 Hamiltonian model for one-and two-qubit gates
116(1)
3.7 Universal quantum gates
117(10)
3.7.1 * Preparation of the initial state
124(3)
3.8 Unitary errors
127(1)
3.9 Function evaluation
128(4)
3.10 * The quantum adder
132(2)
3.11 Adiabatic theorem
134(7)
3.11.1 Adiabatic condition
136(1)
3.11.2 Berry phase
137(4)
3.12 * Non-Abelian geometric phase
141(4)
3.13 Adiabatic quantum computation
145(4)
3.14 * Maximum speed of quantum gates
149(3)
3.14.1 * Speed limit of an autonomous time evolution
150(1)
3.14.2 * Speed limit of single-qubit gates
151(1)
3.15 * Holonomic quantum computation
152(3)
3.16 A guide to the bibliography
155(2)
4 Quantum algorithms 157(38)
4.1 Deutsch's algorithm
157(4)
4.1.1 The Deutsch-Jozsa problem
158(1)
4.1.2 * An extension of Deutsch's algorithm
159(2)
4.2 Quantum search
161(7)
4.2.1 Searching one item out of four
161(2)
4.2.2 Searching one item out of N
163(1)
4.2.3 Geometric visualization
164(2)
4.2.4 Searching by adiabatic quantum evolution
166(2)
4.3 The quantum Fourier transform
168(3)
4.4 Quantum phase estimation
171(2)
4.5 * Finding eigenvalues and eigenvectors
173(2)
4.6 Period finding and Shor's algorithm
175(4)
4.7 Quantum computation of dynamical systems
179(11)
4.7.1 Quantum simulation of the Schrodinger equation
179(4)
4.7.2 * The quantum baker's map
183(2)
4.7.3 * The quantum sawtooth map
185(3)
4.7.4 Information extraction for dynamical quantum systems
188(2)
4.8 Universal quantum simulation
190(2)
4.9 A guide to the bibliography
192(3)
5 Quantum communication 195(46)
5.1 Classical cryptography
195(4)
5.1.1 The Vernam cypher
196(1)
5.1.2 The public-key cryptosystem
197(1)
5.1.3 The RSA protocol
198(1)
5.2 The no-cloning theorem
199(8)
5.2.1 Faster-than-light transmission of information?
201(2)
5.2.2 * The no-signalling condition
203(1)
5.2.3 * Universal quantum cloning
204(2)
5.2.4 * The universal-NOT gate
206(1)
5.3 Quantum cryptography
207(5)
5.3.1 The BB84 protocol
207(3)
5.3.2 The E91 protocol
210(2)
5.4 Dense coding
212(3)
5.5 Quantum teleportation
215(5)
5.5.1 * Conclusive teleportation
219(1)
5.6 Quantum mechanics with continuous variables
220(17)
5.6.1 * General framework for Gaussian states
233(4)
5.7 Quantum cryptography with continuous variables
237(3)
5.8 A guide to the bibliography
240(1)
6 Entanglement and non-classical correlations 241(46)
6.1 Definition of entanglement
241(2)
6.1.1 Basic properties
242(1)
6.2 Bipartite separability criteria
243(5)
6.2.1 The Peres separability criterion
244(1)
6.2.2 Positive maps
245(1)
6.2.3 Entanglement witnesses
246(2)
6.2.4 Positive maps and witnesses
248(1)
6.3 The Shannon entropy
248(4)
6.3.1 Mutual information
250(2)
6.4 The von Neumann entropy
252(4)
6.4.1 Example 1: source of orthogonal pure states
255(1)
6.4.2 Example 2: source of non-orthogonal pure states
255(1)
6.5 Entanglement concentration
256(7)
6.5.1 * Entanglement of a random state
260(3)
6.6 Requirements for bipartite entanglement measures
263(1)
6.7 Other entanglement measures
264(2)
6.7.1 * Concurrence
264(1)
6.7.2 * Negativity
265(1)
6.8 * Multipartite entanglement
266(3)
6.8.1 * Monogamy of entanglement and tangle measures
268(1)
6.9 Quantum discord
269(8)
6.9.1 Definition
270(3)
6.9.2 Basic properties
273(1)
6.9.3 Examples
274(1)
6.9.4 * Other measures of quantum correlations
275(2)
6.10 * Quantum discord in continuous systems
277(2)
6.10.1 * Entropy of a Gaussian state
277(1)
6.10.2 * Discord of a Gaussian state
278(1)
6.11 * Entropies in physics
279(6)
6.11.1 * Thermodynamic entropy
280(2)
6.11.2 * Statistical entropy
282(2)
6.11.3 * Dynamical Kolmogorov-Sinai entropy
284(1)
6.12 A guide to the bibliography
285(2)
7 Decoherence 287(58)
7.1 The Kraus representation
287(6)
7.2 Decoherence models for a single qubit
293(14)
7.2.1 The quantum black box
294(1)
7.2.2 Measuring a quantum operation acting on a qubit
295(1)
7.2.3 Quantum circuits simulating noise channels
296(2)
7.2.4 The bit-flip channel
298(1)
7.2.5 The phase-flip channel
299(1)
7.2.6 The bit-phase-flip channel
300(1)
7.2.7 The depolarizing channel
301(1)
7.2.8 Amplitude damping
302(1)
7.2.9 Phase damping
303(2)
7.2.10 De-entanglement
305(2)
7.3 * The Bloch-Fano representation
307(3)
7.3.1 * Bloch-Fano representation of a state
307(1)
7.3.2 * Bloch-Fano representation of a quantum operation
308(2)
7.4 The master equation
310(14)
7.4.1 * Derivation of the master equation
311(8)
7.4.2 The master equation and quantum operations
319(3)
7.4.3 The master equation for a single qubit
322(2)
7.5 * Non-Markovian quantum dynamics
324(5)
7.6 Quantum to classical transition
329(6)
7.6.1 Schrodinger's cat
329(1)
7.6.2 Decoherence and destruction of cat states
330(5)
7.7 Decoherence and quantum measurements
335(9)
7.7.1 * Weak measurements
337(3)
7.7.2 * Decoherence and quantum trajectories
340(4)
7.8 A guide to the bibliography
344(1)
8 Quantum information theory 345(34)
8.1 Classical data compression
346(5)
8.1.1 Shannon's noiseless coding theorem
346(2)
8.1.2 Examples of data compression
348(1)
8.1.3 Capacity of classical channels
349(2)
8.2 Quantum data compression
351(6)
8.2.1 Schumacher's quantum noiseless coding theorem
351(1)
8.2.2 Compression of an n-qubit message
352(2)
8.2.3 Example 1: two-qubit messages
354(1)
8.2.4 Example 2: three-qubit messages
355(2)
8.3 Accessible information
357(6)
8.3.1 The Holevo bound
358(1)
8.3.2 Example 1: two non-orthogonal pure states
359(3)
8.3.3 * Example 2: three non-orthogonal pure states
362(1)
8.4 Capacities of quantum channels
363(8)
8.4.1 Classical capacity
364(1)
8.4.2 Quantum capacity
365(6)
8.5 * Quantum memory channels
371(7)
8.6 A guide to the bibliography
378(1)
9 Quantum error correction 379(38)
9.1 The three-qubit bit-flip code
381(3)
9.2 The three-qubit phase-flip code
384(1)
9.3 The nine-qubit Shor code
385(4)
9.4 General properties of quantum error correction
389(3)
9.4.1 The quantum Hamming bound
391(1)
9.5 Stabilizer coding
392(4)
9.5.1 The nine-qubit Shor code revisited
392(2)
9.5.2 * General formalism for stabilizer codes
394(1)
9.5.3 * Logical operators for stabilizer codes
395(1)
9.6 * The five-qubit code
396(3)
9.7 Decoherence-free subspaces
399(5)
9.7.1 * Conditions for decoherence-free dynamics
401(1)
9.7.2 * The spin-boson model
402(2)
9.8 * Dynamical decoupling
404(3)
9.8.1 * Explicit form of control Hamiltonian
406(1)
9.9 * The Zeno effect
407(4)
9.10 Fault-tolerant quantum computation
411(4)
9.10.1 Avoidance of error propagation
411(2)
9.10.2 Fault-tolerant quantum gates
413(1)
9.10.3 The noise threshold for quantum computation
414(1)
9.11 A guide to the bibliography
415(2)
10 Principles of experimental implementations of quantum protocols 417(40)
10.1 Cavity quantum electrodynamics
418(6)
10.1.1 Interaction of a two-level atom with a classical field
420(1)
10.1.2 The Jaynes-Cummings model
421(1)
10.1.3 Rabi oscillations
422(1)
10.1.4 Entanglement generation
423(1)
10.2 The ion-trap quantum computer
424(9)
10.2.1 The Paul trap
425(2)
10.2.2 Laser pulses
427(6)
10.3 Solid-state qubits
433(10)
10.3.1 Spins in semiconductors
433(1)
10.3.2 Quantum dots
434(3)
10.3.3 Superconducting qubit circuits
437(6)
10.4 Quantum communication with photons
443(11)
10.4.1 Linear optics
444(2)
10.4.2 Non-linear optics and probabilistic gates
446(3)
10.4.3 Experimental quantum-key distribution
449(5)
10.5 Problems and prospects
454(1)
10.6 A guide to the bibliography
455(2)
11 Quantum information in many-body systems 457(78)
11.1 Quantum simulators
458(8)
11.1.1 Ultracold atoms
458(3)
11.1.2 Arrays of coupled QED cavities
461(5)
11.2 Emergence of quantum correlations
466(3)
11.2.1 The Hubbard model
467(2)
11.3 The spin-1/2 quantum Ising chain
469(15)
11.3.1 Jordan-Wigner transformation
470(2)
11.3.2 Diagonalization of the Ising chain
472(6)
11.3.3 Two-spin concurrence
478(1)
11.3.4 Entanglement block entropy
479(2)
11.3.5 The Ising model revisited: Kitaev chain
481(3)
11.4 Area-law scaling of the entanglement
484(3)
11.5 Matrix product states
487(5)
11.5.1 Examples of MPS wave functions
490(2)
11.6 Graphical representation of matrix product states
492(11)
11.6.1 Expectation values of observables
494(2)
11.6.2 * Scaling of correlation functions with the distance
496(2)
11.6.3 Gauge freedom
498(2)
11.6.4 Schmidt decomposition of a MPS
500(3)
11.7 Ground-state search in the Hilbert space corner
503(9)
11.7.1 Density-matrix renormalization group
506(4)
11.7.2 * DMRG as a variational optimization over the MPS class
510(2)
11.8 Time evolution of matrix product states
512(7)
11.8.1 Finite-temperature calculations
515(2)
11.8.2 Mixed-state time evolution
517(2)
11.9 * General tensor-network structures
519(10)
11.9.1 * Projected entangled pair states
519(5)
11.9.2 * Hierarchical tensor networks
524(5)
11.10 A guide to the bibliography 526 Conclusions and prospects
529(6)
Appendix A: Elements of linear algebra 535(30)
A.1 Finite-dimensional vector spaces
535(22)
A.1.1 Basic properties of vector spaces
535(1)
A.1.2 Inner product and norm of a vector
536(2)
A.1.3 Linear independence and the notion of basis
538(2)
A.1.4 Linear operators
540(5)
A.1.5 Tensor product
545(2)
A.1.6 Matrix decompositions
547(8)
A.1.7 Symplectic decompositions
555(2)
A.2 Infinite-dimensional vector spaces
557(8)
A.2.1 Discrete and continuous bases
557(1)
A.2.2 The Dirac delta function
558(1)
A.2.3 Orthonormality and completeness relations
559(1)
A.2.4 Position and momentum representations
560(3)
A.2.5 Position and momentum operators
563(2)
Appendix B: Solutions to the exercises 565(86)
B.1
Chapter 1
565(1)
B.2
Chapter 2
566(7)
B.3
Chapter 3
573(11)
B.4
Chapter 4
584(1)
B.5
Chapter 5
585(9)
B.6
Chapter 6
594(6)
B.7
Chapter 7
600(15)
B.8
Chapter 8
615(3)
B.9
Chapter 9
618(7)
B.10
Chapter 10
625(19)
B.11
Chapter 11
644(4)
B.12 Appendix A
648(3)
Bibliography 651(26)
Index 677
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