Quantum information processing and quantum error correction pdf
File Name: quantum information processing and quantum error correction .zip
- Quantum error correction
- Quantum error correction
- CMSC 858K: Introduction to quantum information processing (Fall 2016)
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Quantum error correction QEC is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal not only with noise on stored quantum information, but also with faulty quantum gates, faulty quantum preparation, and faulty measurements. Classical error correction employs redundancy.
Quantum error correction
Quantum error correction
CMSC 858K: Introduction to quantum information processing (Fall 2016)
To implement fault-tolerant quantum computation with continuous variables, the Gottesman—Kitaev—Preskill GKP qubit has been recognized as an important technological element. We have proposed a method to reduce the required squeezing level to realize large-scale quantum computation with the GKP qubit [ Phys. X 8 , ], harnessing the virtue of analog information in the GKP qubits. In the present work, to reduce the number of qubits required for large-scale quantum computation, we propose the tracking quantum error correction, where the logical-qubit-level quantum error correction is partially substituted by the single-qubit-level quantum error correction. In the proposed method, the analog quantum error correction is utilized to make the performances of the single-qubit-level quantum error correction almost identical to those of the logical-qubit-level quantum error correction in a practical noise level.
Quantum Information Processing and Quantum Error Correction is a self-contained, tutorial-based introduction to quantum information, quantum computation, and quantum error-correction. Assuming no knowledge of quantum mechanics and written at an intuitive level suitable for the engineer, the book gives all the essential principles needed to design and implement quantum electronic and photonic circuits. Numerous examples from a wide area of application are given to show how the principles can be implemented in practice.
The first 6 chapters were originally prepared in , Chapter 7 was added in , and Chapter 9 was added in A typeset version of Chapter 8 on fault-tolerant quantum computation is not yet available; nor are the figures for Chapter 7. Additional material is available in the form of handwritten notes. Chapters 2 and 3 were updated in July What is now Chapter 5 also updated July is a new version of what was previously the first half of Chapter 6.
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Distributed quantum information processing is based on the transmission of quantum data over lossy channels between quantum processing nodes. Of course, quantum error correction QEC and detection techniques can be used to mitigate such effects, but error detection approaches have severe performance limitations due to the signaling constraints between nodes, and so error correction approaches are preferable—assuming one has sufficient high quality local operations. Typically, performance comparisons between loss-mitigating codes assume one encoded qubit per photon. However, single photons can carry more than one qubit of information and so our focus in this Letter is to explore whether loss-based QEC codes utilizing quantum multiplexed photons are viable and advantageous, especially as photon loss results in more than one qubit of information being lost. We show that quantum multiplexing enables significant resource reduction, in terms of the number of single-photon sources, while at the same time maintaining or even lowering the number of 2-qubit gates required.
Supplemental: Michael A. Nielsen and Isaac L. Copies of both texts will be available on reserve in the Engineering and Physical Sciences Library Math building, room There will be 5 homework assignments during the course.
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Quantum Information Processing, Quantum Computing, and Quantum Error Correction - 2nd Edition - ISBN DRM-free (Mobi, PDF, EPub). × DRM-Free Fault-Tolerant Quantum Error-Correction and Fault-Tolerant Quantum Computing
The Second Edition of Quantum Information Processing, Quantum Computing, and Quantum Error Correction: An Engineering Approach presents a self-contained introduction to all aspects of the area, teaching the essentials such as state vectors, operators, density operators, measurements, and dynamics of a quantum system. In additional to the fundamental principles of quantum computation, basic quantum gates, basic quantum algorithms, and quantum information processing, this edition has been brought fully up to date, outlining the latest research trends. These include:. Quantum error correction codes QECCs , including stabilizer codes, Calderbank-Shor-Steane CSS codes, quantum low-density parity-check LDPC codes, entanglement-assisted QECCs, topological codes, and surface codes Quantum information theory, and quantum key distribution QKD Fault-tolerant information processing and fault-tolerant quantum error correction, together with a chapter on quantum machine learning. Both quantum circuits- and measurement-based quantum computational models are described The next part of the book is spent investigating physical realizations of quantum computers, encoders and decoders; including photonic quantum realization, cavity quantum electrodynamics, and ion traps In-depth analysis of the design and realization of a quantum information processing and quantum error correction circuits. This fully up-to-date new edition will be of use to engineers, computer scientists, optical engineers, physicists and mathematicians.
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