Fault-Tolerant Quantum Computation With Constant Error

Dorit Aharonov, Michael Ben-Or · 1997 · STOC 1997（SIAM J. Comput. 38, 1207 (2008)）

| 编号 QE010 | 主题 基础理论 | 链接 arXiv:quant-ph/9611025 |

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 the past year many developments had taken place in the area of quantum error corrections. Recently Shor showed how to perform fault tolerant quantum computation when, η, the probability for a fault in one time step per qubit or per gate, is logarithmically small. This paper improves this bound and shows how to perform fault tolerant quantum computation when the error probability, η, is smaller than some constant threshold, η 0 . The cost is polylogarithmic in time and space, and no measurements are used during the quantum computation. The same result is shown also for quantum circuits which operate on nearest neighbors only. To achieve this noise resistance, we use concatenated quantum error correcting codes. The scheme presented is general, and works with any quantum code, conditioned that the code satisfies some restrictions, namely that it is a “proper quantum code”. The constant threshold η 0 is a function of the parameters of the specific proper code used. We present two explicit classes of proper quantum codes. The first example of proper quantum codes generalizes classical secret sharing with polynomials. The second uses a known class of quantum codes a

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