Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's ...
More
In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.Less
In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
As computers get faster and faster, the size of the circuitry imprinted onto silicon chips decreases. The size of the circuitry becomes so small that its behavior is governed by the laws of quantum ...
More
As computers get faster and faster, the size of the circuitry imprinted onto silicon chips decreases. The size of the circuitry becomes so small that its behavior is governed by the laws of quantum mechanics. Such a computer, whose computations would be fully quantum mechanical, is called a quantum computer. Any computational task such as addition, multiplication, displaying graphics, or updating databases is performed by a computer according to an algorithm — an abstract set of instructions. Quantum computers would accomplish tasks by performing quantum algorithms. A quantum algorithm is a sequence of unitary evolutions carried out on a quantum string made up of qubits, which can exist as a superposition of classical strings. This chapter discusses the computational complexity of a quantum algorithm, Deutsch's algorithm and its efficiency as quantified by the Holevo bound, Oracles, Grover's search algorithm, quantum factorisation, quantum Fourier transform, and phase estimation.Less
As computers get faster and faster, the size of the circuitry imprinted onto silicon chips decreases. The size of the circuitry becomes so small that its behavior is governed by the laws of quantum mechanics. Such a computer, whose computations would be fully quantum mechanical, is called a quantum computer. Any computational task such as addition, multiplication, displaying graphics, or updating databases is performed by a computer according to an algorithm — an abstract set of instructions. Quantum computers would accomplish tasks by performing quantum algorithms. A quantum algorithm is a sequence of unitary evolutions carried out on a quantum string made up of qubits, which can exist as a superposition of classical strings. This chapter discusses the computational complexity of a quantum algorithm, Deutsch's algorithm and its efficiency as quantified by the Holevo bound, Oracles, Grover's search algorithm, quantum factorisation, quantum Fourier transform, and phase estimation.
Dagmar Bruß and Chiara Macchiavello
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199603657
- eISBN:
- 9780191729515
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199603657.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter contains an introduction to the main concepts in quantum computation and entanglement. It starts with a brief introduction to computational complexity and then introduces quantum gates ...
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This chapter contains an introduction to the main concepts in quantum computation and entanglement. It starts with a brief introduction to computational complexity and then introduces quantum gates and quantum networks, discussing the universality issue in quantum computation. A review on the main known quantum algorithms follows, including Deutsch's, Deutsch-Jozsa's, Grover's and Shor's algorithms. The basic concepts in the theory of quantum error correction are then reviewed. The second part of the chapter is devoted to entanglement. It starts by reminding the basic definitions of entanglement and entanglement criteria for bipartite and multipartite systems, and then discusses the role that entanglement plays in the quantum algorithms described before. The chapter ends with short descriptions of NMR quantum computing, the computational model DQC1, and one-way quantum computing.Less
This chapter contains an introduction to the main concepts in quantum computation and entanglement. It starts with a brief introduction to computational complexity and then introduces quantum gates and quantum networks, discussing the universality issue in quantum computation. A review on the main known quantum algorithms follows, including Deutsch's, Deutsch-Jozsa's, Grover's and Shor's algorithms. The basic concepts in the theory of quantum error correction are then reviewed. The second part of the chapter is devoted to entanglement. It starts by reminding the basic definitions of entanglement and entanglement criteria for bipartite and multipartite systems, and then discusses the role that entanglement plays in the quantum algorithms described before. The chapter ends with short descriptions of NMR quantum computing, the computational model DQC1, and one-way quantum computing.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the ...
More
This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.Less
This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.00012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter introduces a method that combines the concepts of quantum entanglement with those of quantum algorithms. In particular, some bounds are placed on the efficiency (speedup) of quantum ...
More
This chapter introduces a method that combines the concepts of quantum entanglement with those of quantum algorithms. In particular, some bounds are placed on the efficiency (speedup) of quantum computations by using the fact that there is a limit to how quickly entanglement can be generated with some operations. This method will truly exploit the “many-worlds” nature of quantum superpositions. By solving one problem using a superposition of qubits as well as solving a superposition of problems, the efficiency of some quantum tasks can be evaluated. This chapter demonstrates that a quantum search cannot be performed faster than the square root of the time of the corresponding classical search (winch is still very much faster). The use of entanglement to optimise quantum searches is discussed, along with a model for quantum measurement, similarity between quantum computation and a quantum measurement as described by von Neumann, correlations and quantum measurement, and the Bekenstein bound as an example of the ultimate limits of quantum computation.Less
This chapter introduces a method that combines the concepts of quantum entanglement with those of quantum algorithms. In particular, some bounds are placed on the efficiency (speedup) of quantum computations by using the fact that there is a limit to how quickly entanglement can be generated with some operations. This method will truly exploit the “many-worlds” nature of quantum superpositions. By solving one problem using a superposition of qubits as well as solving a superposition of problems, the efficiency of some quantum tasks can be evaluated. This chapter demonstrates that a quantum search cannot be performed faster than the square root of the time of the corresponding classical search (winch is still very much faster). The use of entanglement to optimise quantum searches is discussed, along with a model for quantum measurement, similarity between quantum computation and a quantum measurement as described by von Neumann, correlations and quantum measurement, and the Bekenstein bound as an example of the ultimate limits of quantum computation.
