SIAM Journal on Computing, Volume 49, Issue 6, Page 1423-1427, January 2020.
This note indicates an error in the proof of Theorem 3.1 in [T. Vidick, SIAM J. Comput., 45 (2016), pp. 1007--1063]. Due to an induction step in the soundness analysis not being carried out correctly, the analysis fails to prove the claimed result. The error invalidates the proofs of the main computational hardness results claimed in the paper. We discuss implications for subsequent works. In some cases results can be partially recovered by applying a weakened version of Theorem 3.1 shown in [Z. Ji et al., Quantum Soundness of the Classical Low Individual Degree Test, arXiv:2009.1298, 2020] subsequently to the discovery of the error. The validity of Theorem 3.1 as stated in the paper remains an open question.

中文翻译：

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勘误表：三层纠缠的异或游戏是NP难以近似的

2020年1月，SIAM计算杂志，第49卷，第6期，第1423-1427页。
本注释表示[T. Vidick，SIAM J.Comput。，45（2016），第1007--1063页]。由于未正确执行健全性分析中的归纳步骤，因此该分析无法证明要求保护的结果。该错误使本文所声称的主要计算硬度结果的证明无效。我们讨论对后续工作的影响。在某些情况下，可以通过应用[Z.]中所示的弱化定理3.1来部分恢复结果。在发现错误之后，Ji等人（经典低个体度测试的量子稳健性，arXiv：2009.1298，2020）。如本文所述，定理3.1的有效性仍然是一个悬而未决的问题。