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. http://dx.doi.org/10.1103/PhysRevLett.100.160501 100 http://dx.doi.org/10.1103/PhysRevLett.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 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 Harrow et al (2009 Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.103.150502 103 http://dx.doi.org/10.1103/PhysRevLett.103.150502 ) or quantum machine learning Rebentrost et al (2014 Phys. Rev. Lett. http://dx.doi.org/10.1103/PhysRevLett.113.130503 113 http://dx.doi.org/10.1103/PhysRevLett.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.

Keywords

• quantum memories
• quantum error correction
• quantum algorithms