Quantum computing: from linear algebra to physical realizations
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| Format: | Buch |
| Sprache: | English |
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CRC Press
2008
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| Beschreibung: | XVI, 421 S. |
| ISBN: | 0750309830 9780750309837 |
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| 020 | |a 9780750309837 |9 978-0-7503-0983-7 | ||
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| 100 | 1 | |a Nakahara, Mikio |e Verfasser |0 (DE-588)1028332297 |4 aut | |
| 245 | 1 | 0 | |a Quantum computing |b from linear algebra to physical realizations |c Mikio Nakahara ; Tetsuo Ohmi |
| 264 | 1 | |a Boca Raton, FL. [u.a.] |b CRC Press |c 2008 | |
| 300 | |a XVI, 421 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Quantencomputer |0 (DE-588)4533372-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantencomputer |0 (DE-588)4533372-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ohmi, Tetsuo |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016139077&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016139077 | ||
Datensatz im Suchindex
| _version_ | 1804137167627223040 |
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| adam_text | Contents
I From Linear Algebra to Quantum Computing
1
1
Basics of Vectors and Matrices
3
1.1
Vector Spaces
........................... 4
1.2
Linear Dependence and Independence of Vectors
....... 5
1.3
Dual Vector Spaces
........................ 6
1.4
Basis, Projection Operator and Completeness Relation
.... 8
1.4.1
Orthonormal
Basis and Completeness Relation
.... 8
1.4.2
Projection Operators
................... 9
1.4.3
Gram-Schmidt Orthonormalization
........... 10
1.5
Linear Operators and Matrices
................. 11
1.5.1
Hermitian Conjugate, Hermitian and Unitary
Matrices
.......................... 12
1.6
Eigenvalue Problems
....................... 13
1.6.1
Eigenvalue Problems of Hermitian and Normal
Matrices
.......................... 14
1.7 Pauli
Matrices
.......................... 18
1.8
Spectral Decomposition
..................... 19
1.9
Singular Value Decomposition
(SVD)
.............. 23
1.10
Tensor Product
(Kronecker
Product)
.............. 26
2
Framework of Quantum Mechanics
29
2.1
Fundamental Postulates
..................... 29
2.2
Some Examples
.......................... 32
2.3
Multipartite System, Tensor Product and Entangled State
. . 36
2.4
Mixed States and Density Matrices
............... 38
2.4.1
Negativity
......................... 42
2.4.2
Partial Trace and Purification
.............. 45
2.4.3
Fidelity
.......................... 47
3
Qubits and Quantum Key Distribution
51
3.1
Qubits
............................... 51
3.1.1
One Qubit
......................... 51
3.1.2
Bloch Sphere
....................... 53
3.1.3
Multi-Qubit Systems and Entangled States
...... 54
3.1.4
Measurements
....................... 56
3.1.5
Einstein-Podolsky-
Rosen (EPR) Paradox ....... 59
3.2 Quantum Key Distribution (BB84
Protocol)
.......... 60
4 Quantum Gates, Quantum Circuit and Quantum
Computa¬
tion
65
4.1
Introduction............................
65
4.2 Quantum Gates.......................... 66
4.2.1 Simple Quantum Gates ................. 66
4.2.2 Walsh-Hadamard Transformation............ 69
4.2.3
SWAP Gate
and Fredkin Gate............. 70
4.3
Correspondence with Classical
Logic Gates .......... 71
4.3.1 NOT Gate......................... 72
4.3.2 XOR Gate......................... 72
4.3.3 AND Gate......................... 73
4.3.4
OR
Gate.......................... 73
4.4 No-Cloning Theorem....................... 75
4.5
Dense Coding
and Quantum
Teleportation
........... 76
4.5.1
Dense Coding
....................... 77
4.5.2
Quantum
Teleportation
................. 79
4.6
Universal Quantum Gates
.................... 82
4.7
Quantum Parallelism and Entanglement
............ 95
5
Simple Quantum Algorithms
99
5.1 Deutsch
Algorithm
........................ 99
5.2
Deutsch-Jozsa Algorithm and Bernstein-Vazirani Algorithm
. 101
5.3
Simon s Algorithm
........................ 105
6
Quantum Integral Transforms
109
6.1
Quantum Integral Transforms
.................. 109
6.2
Quantum Fourier Transform (QFT)
..............
Ill
6.3
Application of QFT: Period-Finding
.............. 113
6.4
Implementation of QFT
..................... 116
6.5
Walsh-Hadamard Transform
................... 122
6.6
Selective Phase Rotation Transform
.............. 123
7
Grover s Search Algorithm
125
7.1
Searching for a Single File
.................... 125
7.2
Searching for
d
Files
....................... 133
8
Shor s Factorization Algorithm
137
8.1
The RSA Cryptosystem
..................... 137
8.2
Factorization Algorithm
..................... 140
8.3
Quantum Part of Shor s Algorithm
............... 141
8.3.1
Settings for STEP
2................... 141
8.3.2
STEP
2.......................... 143
8.4
Probability Distribution
..................... 144
8.5
Continued Fractions and Order Finding
............ 151
8.6
Modular Exponential Function
................. 156
8.6.1
Adder
........................... 157
8.6.2
Modular Adder
...................... 161
8.6.3
Modular Multiplexer
................... 166
8.6.4
Modular Exponential Function
............. 168
8.6.5
Computational Complexity of Modular Exponential
Circuit
........................... 170
9
Decoherence
173
9.1
Open Quantum System
..................... 173
9.1.1
Quantum Operations and
Kraus
Operators
...... 174
9.1.2
Operator-Sum Representation and Noisy Quantum
Channel
.......................... 177
9.1.3
Completely Positive Maps
................ 178
9.2
Measurements as Quantum Operations
............. 179
9.2.1
Projective
Measurements
................ 179
9.2.2
POVM
........................... 180
9.3
Examples
............................. 181
9.3.1
Bit-Flip Channel
..................... 181
9.3.2
Phase-Flip Channel
.................... 183
9.3.3
Depolarizing Channel
.................. 185
9.3.4
Amplitude-Damping Channel
.............. 187
9.4
Lindblad
Equation
........................ 188
9.4.1
Quantum Dynamical Semigroup
............ 189
9.4.2
Lindblad
Equation
.................... 189
9.4.3
Examples
......................... 192
10
Quantum Error Correcting Codes
195
10.1
Introduction
............................195
10.2
Three-Qubit Bit-Flip Code and Phase-Flip Code
.......196
10.2.1
Bit-Flip QECC
......................196
10.2.2
Phase-Flip QECC
....................202
10.3
Shor s Nine-Qubit Code
.....................203
10.3.1
Encoding
.........................204
10.3.2
Transmission
.......................205
10.3.3
Error Syndrome Detection and Correction
.......205
10.3.4
Decoding
.........................208
10.4
Seven-Qubit QECC
........................209
10.4.1
Classical Theory of Error Correcting Codes
......209
10.4.2
Seven-Qubit QECC
....................213
10.4.3
Gate Operations for Seven-Qubit QECC
........220
10.5
Five-Qubit QECC
........................224
10.5.1
Encoding
.........................224
10.5.2
Error
Syndrome
Detection
................227
II Physical Realizations of Quantum Computing
231
11
Di Vincenzo
Criteria
233
11.1
Introduction
............................233
11.2
DiVincenzo
Criteria
.......................234
11.3
Physical Realizations
.......................239
12
NMR Quantum Computer
241
12.1
Introduction
............................241
12.2
NMR Spectrometer
........................241
12.2.1
Molecules
.........................242
12.2.2
NMR Spectrometer
....................242
12.3
Hamiltonian
............................245
12.3.1
Single-Spin Hamiltonian
.................245
12.3.2
Multi-Spin Hamiltonian
.................248
12.4
Implementation of Gates and Algorithms
............252
12.4.1
One-Qubit Gates in One-Qubit Molecule
........252
12.4.2
One-Qubit Operation in Two-Qubit Molecule: Bloch-
Siegert Effect
.......................256
12.4.3
Two-Qubit Gates
.....................257
12.4.4
Multi-Qubit Gates
....................259
12.5
Time-Optimal Control of NMR Quantum Computer
.....262
12.5.1
A Brief Introduction to Lie Algebras and Lie Groups
. 262
12.5.2
Cartan Decomposition and Optimal Implementation
of Two-Qubit Gates
...................264
12.6
Measurements
...........................268
12.6.1
Introduction and Preliminary
..............268
12.6.2
One-Qubit Quantum State Tomography
........269
12.6.3
Free Induction Decay (FID)
...............270
12.6.4
Two-Qubit Tomography
.................271
12.7
Preparation of
Pseudopure
State
................274
12.7.1
Temporal Averaging
...................276
12.7.2
Spatial Averaging
.....................277
12.8
DiVincenzo
Criteria
.......................281
13
Trapped Ions
285
13.1
Introduction
............................285
13.2
Electronic States of Ions as Qubits
...............287
13.3
Ions in Paul Trap
.........................289
13.3.1
Trapping Potential
....................289
13.3.2
Lattice Formation
....................294
13.3.3
Normal Modes
......................296
13.4
Ion Qubit
.............................298
13.4.1
One-Spin Hamiltonian
..................298
13.4.2
Sideband Cooling
.....................301
13.5
Quantum Gates
..........................302
13.5.1
One-Qubit Gates
.....................302
13.5.2
CNOT
Gate
........................304
13.6
Readout
..............................306
13.7
DiVincenzo
Criteria
.......................307
14
Quantum Computing with Neutral Atoms
311
14.1
Introduction
............................311
14.2
Trapping Neutral Atoms
.....................311
14.2.1
Alkali Metal Atoms
.................... 311
14.2.2
Magneto-Optical Trap (MOT)
............. 312
14.2.3
Optical
Dipole
Trap
................... 314
14.2.4
Optical Lattice
...................... 316
14.2.5
Spin-Dependent Optical Potential
............ 317
14.3
One-Qubit Gates
......................... 319
14.4
Quantum State Engineering of Neutral Atoms
......... 321
14.4.1
Trapping of a Single Atom
................ 321
14.4.2
Rabi
Oscillation
...................... 321
14.4.3
Neutral Atom Quantum Regisiter
............ 323
14.5
Preparation of Entangled Neutral Atoms
............ 324
14.6
DiVincenzo
Criteria
....................... 327
15
Josephson
Junction Qubits
329
15.1
Introduction
............................329
15.2
Nanoscale
Josephson
Junctions and SQUIDs
..........330
15.2.1
Josephson
Junctions
...................330
15.2.2
SQUIDs
..........................333
15.3
Charge Qubit
...........................337
15.3.1
Simple Cooper Pair Box
.................337
15.3.2
Split Cooper Pair Box
..................341
15.4
Flux Qubit
............................342
15.4.1
Simplest Flux Qubit
...................342
15.4.2
Three-Junction Flux Qubit
...............345
15.5
Quantronium
...........................347
15.6
Current-Biased Qubit (Phase Qubit)
..............348
15.7
Readout
..............................352
15.7.1
Charge Qubit
.......................352
15.7.2
Readout of Quantronium
................355
15.7.3
Switching Current Readout of Flux Qubits
......357
15.8
Coupled Qubits
..........................358
15.8.1
Capacitively Coupled Charge Qubits
..........359
15.8.2
Inductive Coupling of Charge Qubits
..........362
15.8.3
Tunable Coupling between Flux Qubits
........366
15.8.4
Coupling Flux Qubits with an LC Resonator
.....369
15.9
DiVincenzo
Criteria
.......................374
16
Quantum Computing with Quantum Dots
377
16.1
Introduction
............................377
16.2
Mesoscopic Semiconductors
...................377
16.2.1
Two-Dimensional Electron Gas in Inversion Layer
. . 377
16.2.2
Coulomb Blockade
....................378
16.3
Electron Charge Qubit
......................383
16.3.1
Electron Charge Qubit
..................384
16.3.2
Rabi
Oscillation
......................385
16.4
Electron Spin Qubit
.......................386
16.4.1
Electron Spin Qubit
...................386
16.4.2
Single-Qubit Operations
.................387
16.4.3
Coherence Time
.....................390
16.5
DiVincenzo
Criteria
.......................396
16.5.1
Charge Qubits
......................396
16.5.2
Spin Qubits
........................397
A Solutions to Selected Exercises
399
Index
417
|
| adam_txt |
Contents
I From Linear Algebra to Quantum Computing
1
1
Basics of Vectors and Matrices
3
1.1
Vector Spaces
. 4
1.2
Linear Dependence and Independence of Vectors
. 5
1.3
Dual Vector Spaces
. 6
1.4
Basis, Projection Operator and Completeness Relation
. 8
1.4.1
Orthonormal
Basis and Completeness Relation
. 8
1.4.2
Projection Operators
. 9
1.4.3
Gram-Schmidt Orthonormalization
. 10
1.5
Linear Operators and Matrices
. 11
1.5.1
Hermitian Conjugate, Hermitian and Unitary
Matrices
. 12
1.6
Eigenvalue Problems
. 13
1.6.1
Eigenvalue Problems of Hermitian and Normal
Matrices
. 14
1.7 Pauli
Matrices
. 18
1.8
Spectral Decomposition
. 19
1.9
Singular Value Decomposition
(SVD)
. 23
1.10
Tensor Product
(Kronecker
Product)
. 26
2
Framework of Quantum Mechanics
29
2.1
Fundamental Postulates
. 29
2.2
Some Examples
. 32
2.3
Multipartite System, Tensor Product and Entangled State
. . 36
2.4
Mixed States and Density Matrices
. 38
2.4.1
Negativity
. 42
2.4.2
Partial Trace and Purification
. 45
2.4.3
Fidelity
. 47
3
Qubits and Quantum Key Distribution
51
3.1
Qubits
. 51
3.1.1
One Qubit
. 51
3.1.2
Bloch Sphere
. 53
3.1.3
Multi-Qubit Systems and Entangled States
. 54
3.1.4
Measurements
. 56
3.1.5
Einstein-Podolsky-
Rosen (EPR) Paradox . 59
3.2 Quantum Key Distribution (BB84
Protocol)
. 60
4 Quantum Gates, Quantum Circuit and Quantum
Computa¬
tion
65
4.1
Introduction.
65
4.2 Quantum Gates. 66
4.2.1 Simple Quantum Gates . 66
4.2.2 Walsh-Hadamard Transformation. 69
4.2.3
SWAP Gate
and Fredkin Gate. 70
4.3
Correspondence with Classical
Logic Gates . 71
4.3.1 NOT Gate. 72
4.3.2 XOR Gate. 72
4.3.3 AND Gate. 73
4.3.4
OR
Gate. 73
4.4 No-Cloning Theorem. 75
4.5
Dense Coding
and Quantum
Teleportation
. 76
4.5.1
Dense Coding
. 77
4.5.2
Quantum
Teleportation
. 79
4.6
Universal Quantum Gates
. 82
4.7
Quantum Parallelism and Entanglement
. 95
5
Simple Quantum Algorithms
99
5.1 Deutsch
Algorithm
. 99
5.2
Deutsch-Jozsa Algorithm and Bernstein-Vazirani Algorithm
. 101
5.3
Simon's Algorithm
. 105
6
Quantum Integral Transforms
109
6.1
Quantum Integral Transforms
. 109
6.2
Quantum Fourier Transform (QFT)
.
Ill
6.3
Application of QFT: Period-Finding
. 113
6.4
Implementation of QFT
. 116
6.5
Walsh-Hadamard Transform
. 122
6.6
Selective Phase Rotation Transform
. 123
7
Grover's Search Algorithm
125
7.1
Searching for a Single File
. 125
7.2
Searching for
d
Files
. 133
8
Shor's Factorization Algorithm
137
8.1
The RSA Cryptosystem
. 137
8.2
Factorization Algorithm
. 140
8.3
Quantum Part of Shor's Algorithm
. 141
8.3.1
Settings for STEP
2. 141
8.3.2
STEP
2. 143
8.4
Probability Distribution
. 144
8.5
Continued Fractions and Order Finding
. 151
8.6
Modular Exponential Function
. 156
8.6.1
Adder
. 157
8.6.2
Modular Adder
. 161
8.6.3
Modular Multiplexer
. 166
8.6.4
Modular Exponential Function
. 168
8.6.5
Computational Complexity of Modular Exponential
Circuit
. 170
9
Decoherence
173
9.1
Open Quantum System
. 173
9.1.1
Quantum Operations and
Kraus
Operators
. 174
9.1.2
Operator-Sum Representation and Noisy Quantum
Channel
. 177
9.1.3
Completely Positive Maps
. 178
9.2
Measurements as Quantum Operations
. 179
9.2.1
Projective
Measurements
. 179
9.2.2
POVM
. 180
9.3
Examples
. 181
9.3.1
Bit-Flip Channel
. 181
9.3.2
Phase-Flip Channel
. 183
9.3.3
Depolarizing Channel
. 185
9.3.4
Amplitude-Damping Channel
. 187
9.4
Lindblad
Equation
. 188
9.4.1
Quantum Dynamical Semigroup
. 189
9.4.2
Lindblad
Equation
. 189
9.4.3
Examples
. 192
10
Quantum Error Correcting Codes
195
10.1
Introduction
.195
10.2
Three-Qubit Bit-Flip Code and Phase-Flip Code
.196
10.2.1
Bit-Flip QECC
.196
10.2.2
Phase-Flip QECC
.202
10.3
Shor's Nine-Qubit Code
.203
10.3.1
Encoding
.204
10.3.2
Transmission
.205
10.3.3
Error Syndrome Detection and Correction
.205
10.3.4
Decoding
.208
10.4
Seven-Qubit QECC
.209
10.4.1
Classical Theory of Error Correcting Codes
.209
10.4.2
Seven-Qubit QECC
.213
10.4.3
Gate Operations for Seven-Qubit QECC
.220
10.5
Five-Qubit QECC
.224
10.5.1
Encoding
.224
10.5.2
Error
Syndrome
Detection
.227
II Physical Realizations of Quantum Computing
231
11
Di Vincenzo
Criteria
233
11.1
Introduction
.233
11.2
DiVincenzo
Criteria
.234
11.3
Physical Realizations
.239
12
NMR Quantum Computer
241
12.1
Introduction
.241
12.2
NMR Spectrometer
.241
12.2.1
Molecules
.242
12.2.2
NMR Spectrometer
.242
12.3
Hamiltonian
.245
12.3.1
Single-Spin Hamiltonian
.245
12.3.2
Multi-Spin Hamiltonian
.248
12.4
Implementation of Gates and Algorithms
.252
12.4.1
One-Qubit Gates in One-Qubit Molecule
.252
12.4.2
One-Qubit Operation in Two-Qubit Molecule: Bloch-
Siegert Effect
.256
12.4.3
Two-Qubit Gates
.257
12.4.4
Multi-Qubit Gates
.259
12.5
Time-Optimal Control of NMR Quantum Computer
.262
12.5.1
A Brief Introduction to Lie Algebras and Lie Groups
. 262
12.5.2
Cartan Decomposition and Optimal Implementation
of Two-Qubit Gates
.264
12.6
Measurements
.268
12.6.1
Introduction and Preliminary
.268
12.6.2
One-Qubit Quantum State Tomography
.269
12.6.3
Free Induction Decay (FID)
.270
12.6.4
Two-Qubit Tomography
.271
12.7
Preparation of
Pseudopure
State
.274
12.7.1
Temporal Averaging
.276
12.7.2
Spatial Averaging
.277
12.8
DiVincenzo
Criteria
.281
13
Trapped Ions
285
13.1
Introduction
.285
13.2
Electronic States of Ions as Qubits
.287
13.3
Ions in Paul Trap
.289
13.3.1
Trapping Potential
.289
13.3.2
Lattice Formation
.294
13.3.3
Normal Modes
.296
13.4
Ion Qubit
.298
13.4.1
One-Spin Hamiltonian
.298
13.4.2
Sideband Cooling
.301
13.5
Quantum Gates
.302
13.5.1
One-Qubit Gates
.302
13.5.2
CNOT
Gate
.304
13.6
Readout
.306
13.7
DiVincenzo
Criteria
.307
14
Quantum Computing with Neutral Atoms
311
14.1
Introduction
.311
14.2
Trapping Neutral Atoms
.311
14.2.1
Alkali Metal Atoms
. 311
14.2.2
Magneto-Optical Trap (MOT)
. 312
14.2.3
Optical
Dipole
Trap
. 314
14.2.4
Optical Lattice
. 316
14.2.5
Spin-Dependent Optical Potential
. 317
14.3
One-Qubit Gates
. 319
14.4
Quantum State Engineering of Neutral Atoms
. 321
14.4.1
Trapping of a Single Atom
. 321
14.4.2
Rabi
Oscillation
. 321
14.4.3
Neutral Atom Quantum Regisiter
. 323
14.5
Preparation of Entangled Neutral Atoms
. 324
14.6
DiVincenzo
Criteria
. 327
15
Josephson
Junction Qubits
329
15.1
Introduction
.329
15.2
Nanoscale
Josephson
Junctions and SQUIDs
.330
15.2.1
Josephson
Junctions
.330
15.2.2
SQUIDs
.333
15.3
Charge Qubit
.337
15.3.1
Simple Cooper Pair Box
.337
15.3.2
Split Cooper Pair Box
.341
15.4
Flux Qubit
.342
15.4.1
Simplest Flux Qubit
.342
15.4.2
Three-Junction Flux Qubit
.345
15.5
Quantronium
.347
15.6
Current-Biased Qubit (Phase Qubit)
.348
15.7
Readout
.352
15.7.1
Charge Qubit
.352
15.7.2
Readout of Quantronium
.355
15.7.3
Switching Current Readout of Flux Qubits
.357
15.8
Coupled Qubits
.358
15.8.1
Capacitively Coupled Charge Qubits
.359
15.8.2
Inductive Coupling of Charge Qubits
.362
15.8.3
Tunable Coupling between Flux Qubits
.366
15.8.4
Coupling Flux Qubits with an LC Resonator
.369
15.9
DiVincenzo
Criteria
.374
16
Quantum Computing with Quantum Dots
377
16.1
Introduction
.377
16.2
Mesoscopic Semiconductors
.377
16.2.1
Two-Dimensional Electron Gas in Inversion Layer
. . 377
16.2.2
Coulomb Blockade
.378
16.3
Electron Charge Qubit
.383
16.3.1
Electron Charge Qubit
.384
16.3.2
Rabi
Oscillation
.385
16.4
Electron Spin Qubit
.386
16.4.1
Electron Spin Qubit
.386
16.4.2
Single-Qubit Operations
.387
16.4.3
Coherence Time
.390
16.5
DiVincenzo
Criteria
.396
16.5.1
Charge Qubits
.396
16.5.2
Spin Qubits
.397
A Solutions to Selected Exercises
399
Index
417 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Nakahara, Mikio Ohmi, Tetsuo |
| author_GND | (DE-588)1028332297 |
| author_facet | Nakahara, Mikio Ohmi, Tetsuo |
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| author_sort | Nakahara, Mikio |
| author_variant | m n mn t o to |
| building | Verbundindex |
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| dewey-ones | 004 - Computer science |
| dewey-raw | 004.1 |
| dewey-search | 004.1 |
| dewey-sort | 14.1 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| discipline_str_mv | Informatik |
| format | Book |
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| id | DE-604.BV022934300 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:55:42Z |
| indexdate | 2024-07-09T21:08:00Z |
| institution | BVB |
| isbn | 0750309830 9780750309837 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016139077 |
| oclc_num | 254253786 |
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| physical | XVI, 421 S. |
| publishDate | 2008 |
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| publisher | CRC Press |
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| spelling | Nakahara, Mikio Verfasser (DE-588)1028332297 aut Quantum computing from linear algebra to physical realizations Mikio Nakahara ; Tetsuo Ohmi Boca Raton, FL. [u.a.] CRC Press 2008 XVI, 421 S. txt rdacontent n rdamedia nc rdacarrier Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quantencomputer (DE-588)4533372-5 s DE-604 Ohmi, Tetsuo Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016139077&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nakahara, Mikio Ohmi, Tetsuo Quantum computing from linear algebra to physical realizations Quantencomputer (DE-588)4533372-5 gnd |
| subject_GND | (DE-588)4533372-5 |
| title | Quantum computing from linear algebra to physical realizations |
| title_auth | Quantum computing from linear algebra to physical realizations |
| title_exact_search | Quantum computing from linear algebra to physical realizations |
| title_exact_search_txtP | Quantum computing from linear algebra to physical realizations |
| title_full | Quantum computing from linear algebra to physical realizations Mikio Nakahara ; Tetsuo Ohmi |
| title_fullStr | Quantum computing from linear algebra to physical realizations Mikio Nakahara ; Tetsuo Ohmi |
| title_full_unstemmed | Quantum computing from linear algebra to physical realizations Mikio Nakahara ; Tetsuo Ohmi |
| title_short | Quantum computing |
| title_sort | quantum computing from linear algebra to physical realizations |
| title_sub | from linear algebra to physical realizations |
| topic | Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | Quantencomputer |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016139077&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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