Quantum error correction: symmetric, asymmetric, synchronizable, and convolutional codes
This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS), Hermitian, and Steane enlargement constructions to certain classes of classical codes. In addition, the bo...
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2020]
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| Schriftenreihe: | Quantum Science and Technology
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| Schlagworte: | |
| Zusammenfassung: | This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS), Hermitian, and Steane enlargement constructions to certain classes of classical codes. In addition, the book presents families of asymmetric quantum codes with good parameters and provides a detailed description of the procedures adopted to construct families of asymmetric quantum convolutional codes.Featuring accessible language and clear explanations, the book is suitable for use in advanced undergraduate and graduate courses as well as for self-guided study and reference. It provides an expert introduction to algebraic techniques of code construction and, because all of the constructions are performed algebraically, it enables the reader to construct families of codes, rather than only codes with specific parameters. The text offers an abundance of worked examples, exercises, and open-ended problems to motivate the reader to further investigate this rich area of inquiry. End-of-chapter summaries and a glossary of key terms allow for easy review and reference |
| Beschreibung: | This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS) construction, the Hermitian, and the Steane’s enlargement construction to certain classes of classical codes. These quantum codes have good parameters and have been introduced recently in the literature. In addition, the book presents families of asymmetric quantum codes with good parameters and provides a detailed description of the procedures adopted to construct families of asymmetric quantum convolutional codes.Featuring accessible language and clear explanations, the book is suitable for use in advanced undergraduate and graduate courses as well as for self-guided study and reference. It provides an expert introduction to algebraic techniques of code construction and, because all of the constructions are performed algebraically, it equips the reader to construct families of codes, rather than only codes with specific parameters. The text offers an abundance of worked examples, exercises, and open-ended problems to motivate the reader to further investigate this rich area of inquiry. End-of-chapter summaries and a glossary of key terms allow for easy review and reference 1-Introduction to quantum mechanics; 1.1-Vector spaces; 1.2- Bases, norms, inner products; 1.3- Linear Operators; 1.4-Eigenvalues and eigenvectors; 1.5- Adjoint, Hermitian and Unitary operators; 1.6- Operator functions; 1.7- Pauli and generalized Pauli matrices; 1.8- Postulates of quantum mechanics; 2-Introduction to quantum computation and information; 2.1-Single and multiple qubit operations; 2.2-Universal quantum gates; 2.3- Bit flip and phase shift channels; 2.4- Depolarizing channel; 2.5-Amplitude damping channel; 2.6-Measure of distance of quantum states; 2.7-Fidelity; 3-Quantum error-correcting codes; 3.1-The Shor code; 3.2-The Steane code; 3.3-Five quibit code; 3.4-Quantum Hamming and Singleton bound; 3.4-Stabilizer codes; 3.5-Calderbank-Shor-Steane code construction; 3.6-Hermitian construction; 3.7-Ste; ane’s enlargement construction; 3.8-Additive codes; 4-Quantum code construction; 4.1-Bose-Chaudhuri-Hocquenghem codes; 4.2-Reed-Solomon codes; 4.3-Reed-Muller codes; 4.4-Quadratic residue codes; 4.5-Constacyclic codes; 4.6- Affine Invariant codes; 4.7-Algebraic geometry codes; 4.8-Synchronizable codes; 5-Asymmetric quantum code construction; 5.1- Bose-Chaudhuri-Hocquenghem codes ; 5.2- Reed-Solomon codes; 5.3-Tensor product codes; 5.4-Alternalt codes; 5.5- Algebraic geometry codes; 5.6-New codes from old; 6-Quantum convolutional code construction; 6.1-Convolutional codes; 6.2-Quantum convolutional codes; 6.3- Code construction: Bose-Chaudhuri-Hocquenghem,; Reed-Solomon; Reed-Muller; 6.4-Construction of asymmetric quantum convolutional codes |
| Beschreibung: | xiii, 227 Seiten 235 mm |
| ISBN: | 9783030485504 9783030485535 |
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| 500 | |a This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS) construction, the Hermitian, and the Steane’s enlargement construction to certain classes of classical codes. These quantum codes have good parameters and have been introduced recently in the literature. In addition, the book presents families of asymmetric quantum codes with good parameters and provides a detailed description of the procedures adopted to construct families of asymmetric quantum convolutional codes.Featuring accessible language and clear explanations, the book is suitable for use in advanced undergraduate and graduate courses as well as for self-guided study and reference. It provides an expert introduction to algebraic techniques of code construction and, because all of the constructions are performed algebraically, it equips the reader to construct families of codes, rather than only codes with specific parameters. The text offers an abundance of worked examples, exercises, and open-ended problems to motivate the reader to further investigate this rich area of inquiry. End-of-chapter summaries and a glossary of key terms allow for easy review and reference | ||
| 500 | |a 1-Introduction to quantum mechanics; 1.1-Vector spaces; 1.2- Bases, norms, inner products; 1.3- Linear Operators; 1.4-Eigenvalues and eigenvectors; 1.5- Adjoint, Hermitian and Unitary operators; 1.6- Operator functions; 1.7- Pauli and generalized Pauli matrices; 1.8- Postulates of quantum mechanics; 2-Introduction to quantum computation and information; 2.1-Single and multiple qubit operations; 2.2-Universal quantum gates; 2.3- Bit flip and phase shift channels; 2.4- Depolarizing channel; 2.5-Amplitude damping channel; 2.6-Measure of distance of quantum states; 2.7-Fidelity; 3-Quantum error-correcting codes; 3.1-The Shor code; 3.2-The Steane code; 3.3-Five quibit code; 3.4-Quantum Hamming and Singleton bound; 3.4-Stabilizer codes; 3.5-Calderbank-Shor-Steane code construction; 3.6-Hermitian construction; 3.7-Ste; ane’s enlargement construction; 3.8-Additive codes; 4-Quantum code construction; 4.1-Bose-Chaudhuri-Hocquenghem codes; 4.2-Reed-Solomon codes; 4.3-Reed-Muller codes; 4.4-Quadratic residue codes; 4.5-Constacyclic codes; 4.6- Affine Invariant codes; 4.7-Algebraic geometry codes; 4.8-Synchronizable codes; 5-Asymmetric quantum code construction; 5.1- Bose-Chaudhuri-Hocquenghem codes ; 5.2- Reed-Solomon codes; 5.3-Tensor product codes; 5.4-Alternalt codes; 5.5- Algebraic geometry codes; 5.6-New codes from old; 6-Quantum convolutional code construction; 6.1-Convolutional codes; 6.2-Quantum convolutional codes; 6.3- Code construction: Bose-Chaudhuri-Hocquenghem,; Reed-Solomon; Reed-Muller; 6.4-Construction of asymmetric quantum convolutional codes | ||
| 520 | |a This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS), Hermitian, and Steane enlargement constructions to certain classes of classical codes. In addition, the book presents families of asymmetric quantum codes with good parameters and provides a detailed description of the procedures adopted to construct families of asymmetric quantum convolutional codes.Featuring accessible language and clear explanations, the book is suitable for use in advanced undergraduate and graduate courses as well as for self-guided study and reference. It provides an expert introduction to algebraic techniques of code construction and, because all of the constructions are performed algebraically, it enables the reader to construct families of codes, rather than only codes with specific parameters. The text offers an abundance of worked examples, exercises, and open-ended problems to motivate the reader to further investigate this rich area of inquiry. End-of-chapter summaries and a glossary of key terms allow for easy review and reference | ||
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Datensatz im Suchindex
| _version_ | 1804181573826772992 |
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| discipline | Informatik |
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| id | DE-604.BV046787244 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T14:51:55Z |
| indexdate | 2024-07-10T08:53:49Z |
| institution | BVB |
| isbn | 9783030485504 9783030485535 |
| language | English |
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| physical | xiii, 227 Seiten 235 mm |
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| series2 | Quantum Science and Technology |
| spelling | Guardia, Guiliano Gadioli La Verfasser aut Quantum error correction symmetric, asymmetric, synchronizable, and convolutional codes Cham Springer [2020] xiii, 227 Seiten 235 mm txt rdacontent n rdamedia nc rdacarrier Quantum Science and Technology This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS) construction, the Hermitian, and the Steane’s enlargement construction to certain classes of classical codes. These quantum codes have good parameters and have been introduced recently in the literature. In addition, the book presents families of asymmetric quantum codes with good parameters and provides a detailed description of the procedures adopted to construct families of asymmetric quantum convolutional codes.Featuring accessible language and clear explanations, the book is suitable for use in advanced undergraduate and graduate courses as well as for self-guided study and reference. It provides an expert introduction to algebraic techniques of code construction and, because all of the constructions are performed algebraically, it equips the reader to construct families of codes, rather than only codes with specific parameters. The text offers an abundance of worked examples, exercises, and open-ended problems to motivate the reader to further investigate this rich area of inquiry. End-of-chapter summaries and a glossary of key terms allow for easy review and reference 1-Introduction to quantum mechanics; 1.1-Vector spaces; 1.2- Bases, norms, inner products; 1.3- Linear Operators; 1.4-Eigenvalues and eigenvectors; 1.5- Adjoint, Hermitian and Unitary operators; 1.6- Operator functions; 1.7- Pauli and generalized Pauli matrices; 1.8- Postulates of quantum mechanics; 2-Introduction to quantum computation and information; 2.1-Single and multiple qubit operations; 2.2-Universal quantum gates; 2.3- Bit flip and phase shift channels; 2.4- Depolarizing channel; 2.5-Amplitude damping channel; 2.6-Measure of distance of quantum states; 2.7-Fidelity; 3-Quantum error-correcting codes; 3.1-The Shor code; 3.2-The Steane code; 3.3-Five quibit code; 3.4-Quantum Hamming and Singleton bound; 3.4-Stabilizer codes; 3.5-Calderbank-Shor-Steane code construction; 3.6-Hermitian construction; 3.7-Ste; ane’s enlargement construction; 3.8-Additive codes; 4-Quantum code construction; 4.1-Bose-Chaudhuri-Hocquenghem codes; 4.2-Reed-Solomon codes; 4.3-Reed-Muller codes; 4.4-Quadratic residue codes; 4.5-Constacyclic codes; 4.6- Affine Invariant codes; 4.7-Algebraic geometry codes; 4.8-Synchronizable codes; 5-Asymmetric quantum code construction; 5.1- Bose-Chaudhuri-Hocquenghem codes ; 5.2- Reed-Solomon codes; 5.3-Tensor product codes; 5.4-Alternalt codes; 5.5- Algebraic geometry codes; 5.6-New codes from old; 6-Quantum convolutional code construction; 6.1-Convolutional codes; 6.2-Quantum convolutional codes; 6.3- Code construction: Bose-Chaudhuri-Hocquenghem,; Reed-Solomon; Reed-Muller; 6.4-Construction of asymmetric quantum convolutional codes This text presents an algebraic approach to the construction of several important families of quantum codes derived from classical codes by applying the well-known Calderbank-Shor-Steane (CSS), Hermitian, and Steane enlargement constructions to certain classes of classical codes. In addition, the book presents families of asymmetric quantum codes with good parameters and provides a detailed description of the procedures adopted to construct families of asymmetric quantum convolutional codes.Featuring accessible language and clear explanations, the book is suitable for use in advanced undergraduate and graduate courses as well as for self-guided study and reference. It provides an expert introduction to algebraic techniques of code construction and, because all of the constructions are performed algebraically, it enables the reader to construct families of codes, rather than only codes with specific parameters. The text offers an abundance of worked examples, exercises, and open-ended problems to motivate the reader to further investigate this rich area of inquiry. End-of-chapter summaries and a glossary of key terms allow for easy review and reference bicssc bisacsh Quantum computers Spintronics Coding theory Information theory Electrical engineering Physics Fehlerbehandlung (DE-588)4153834-1 gnd rswk-swf Quantencomputer (DE-588)4533372-5 gnd rswk-swf Hardcover, Softcover / Physik, Astronomie/Theoretische Physik Quantencomputer (DE-588)4533372-5 s Fehlerbehandlung (DE-588)4153834-1 s DE-604 Erscheint auch als Online-Ausgabe 978-3-030-48551-1 |
| spellingShingle | Guardia, Guiliano Gadioli La Quantum error correction symmetric, asymmetric, synchronizable, and convolutional codes bicssc bisacsh Quantum computers Spintronics Coding theory Information theory Electrical engineering Physics Fehlerbehandlung (DE-588)4153834-1 gnd Quantencomputer (DE-588)4533372-5 gnd |
| subject_GND | (DE-588)4153834-1 (DE-588)4533372-5 |
| title | Quantum error correction symmetric, asymmetric, synchronizable, and convolutional codes |
| title_auth | Quantum error correction symmetric, asymmetric, synchronizable, and convolutional codes |
| title_exact_search | Quantum error correction symmetric, asymmetric, synchronizable, and convolutional codes |
| title_exact_search_txtP | Quantum error correction symmetric, asymmetric, synchronizable, and convolutional codes |
| title_full | Quantum error correction symmetric, asymmetric, synchronizable, and convolutional codes |
| title_fullStr | Quantum error correction symmetric, asymmetric, synchronizable, and convolutional codes |
| title_full_unstemmed | Quantum error correction symmetric, asymmetric, synchronizable, and convolutional codes |
| title_short | Quantum error correction |
| title_sort | quantum error correction symmetric asymmetric synchronizable and convolutional codes |
| title_sub | symmetric, asymmetric, synchronizable, and convolutional codes |
| topic | bicssc bisacsh Quantum computers Spintronics Coding theory Information theory Electrical engineering Physics Fehlerbehandlung (DE-588)4153834-1 gnd Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | bicssc bisacsh Quantum computers Spintronics Coding theory Information theory Electrical engineering Physics Fehlerbehandlung Quantencomputer |
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