A Theory of Fault-Tolerant Quantum Computation

Daniel Gottesman · 1998 · Phys. Rev. A 57, 127

| 编号 QE012 | 主题 基础理论 | 链接 arXiv:quant-ph/9702029 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant operations based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a given code. I demonstrate that fault-tolerant universal computation is possible for any stabilizer code. I discuss a number of examples in more detail, including the five-qubit code. 03.65.Bz,89.80.+h Typeset using REVT E X The development of quantum error-correcting codes [1–6] has stirred great hopes for conquering errors and decoherence in quantum computers. However, just the existence of codes, even very good codes, is not suficient. It is also necessary to be able to perform operations on encoded states without a catastrophic spread of existing errors. However, until now, it was only known how to implement a universal set of gates fault-tolerantly on a few codes [7–9]. While a general formalism for quantum error-correcting codes is known, the code stabilizer [4–6], the theory of fa

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