We study the robustness of the bucket brigade quantum random access memory
model introduced by Giovannetti, Lloyd, and Maccone [Phys. Rev. Lett. 100,
160501 (2008)]. Due to a result of Regev and Schiff [ICALP '08 pp. 773], we
show that for a class of error models the error rate per gate in the bucket
brigade quantum memory has to be of order $o(2^{-n/2})$ (where $N=2^n$ is the
size of the memory) whenever the memory is used as an oracle for the quantum
searching problem. We conjecture that this is the case for any realistic error
model that will be encountered in practice, and that for algorithms with
super-polynomially many oracle queries the error rate must be
super-polynomially small, which further motivates the need for quantum error
correction. By contrast, for algorithms such as matrix inversion [Phys. Rev.
Lett. 103, 150502 (2009)] or quantum machine learning [Phys. Rev. Lett. 113,
130503 (2014)] that only require a polynomial number of queries, the error rate
only needs to be polynomially small and quantum error correction may not be
required. We introduce a circuit model for the quantum bucket brigade
architecture and argue that quantum error correction for the circuit causes the
quantum bucket brigade architecture to lose its primary advantage of a small
number of "active" gates, since all components have to be actively error
corrected.

本文研究了量子存储器的稳健性及其在量子搜索中的应用，发现一个逼真的错误模型需要经受超多项式查询错误率的超多项式下降。因此，本文推测对于任何实际错误模型，其错误率都必须超过多项式，特别是对于超多项式查询的算法，需要超多项式降低错误率，进一步说明量子纠错的必要性。