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The idiots guide to Quantum Error Correction

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Author:  Simon J. Devitt, Kae Nemoto, William J. Munro 
















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Abstract: Quantum Error Correction and faulttolerant quantum computation represent arguably the most vital theoretical aspect of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large scale quantum computers. The introduction of Quantum Error Correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, Quantum Error Correction and faulttolerant computation is now a much more mature field and many new codes, techniques and methodologies have been developed to implement error correction for large scale quantum algorithms. This development has been so pronounced that many in the field of quantum information, specifically those new to quantum information or those focused on the many other important issues in quantum computation have not been able to keep up with the general formalisms and methodologies employed in this area. In response we have attempted to summarize the basic aspects of Quantum Error Correction and faulttolerance, not as a detailed guide, but rather as a basic introduction. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and faulttolerance largely through detailed examples, progressing from basic examples of the 3qubit code through to the stabilizer formalism which is now extremely important when understanding large scale concatenated code structures, quantum circuit synthesis and the more recent developments in subsystem and topological codes. 

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