On the robustness of bucket brigade quantum RAM

Abstract

We study the robustness of the bucket brigade quantum random access memory model introduced by Giovannetti et al (2008 Phys. Rev. Lett.100 160501). Due to a result of Regev and Schiff (ICALP '08 733), 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 superpolynomially 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 Harrow et al (2009 Phys. Rev. Lett.103 150502) or quantum machine learning Rebentrost et al (2014 Phys. Rev. Lett.113 130503) 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.

Hardware-Efficient Quantum Random Access Memory with Hybrid Quantum Acoustic Systems

“…Error resilience. Because our implementation follows the bucket-brigade model, it inherits a favorable log N error scaling [35,36,62]. In particular, the scaling argument of Ref.…”

Optimal usage of quantum random access memory in quantum machine learning

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Time–space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2

“…In this work however, we do not consider BHT as a candidate algorithm for the following reasons. One is that the algorithm entails a need for quantum memory where the realization and the usage cost are controversial [5], and the other is that we are unable to come up with any implementation restricted to use of elementary gates that do not exceed the total cost of O(N 1/2 ).…”