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On the Robustness of Bucket Brigade Quantum RAM

Authors Srinivasan Arunachalam, Vlad Gheorghiu, Tomas Jochym-O'Connor, Michele Mosca, Priyaa Varshinee Srinivasan

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Srinivasan Arunachalam
Vlad Gheorghiu
Tomas Jochym-O'Connor
Michele Mosca
Priyaa Varshinee Srinivasan

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Srinivasan Arunachalam, Vlad Gheorghiu, Tomas Jochym-O'Connor, Michele Mosca, and Priyaa Varshinee Srinivasan. On the Robustness of Bucket Brigade Quantum RAM. In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. 226-244, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.TQC.2015.226

Abstract

We study the robustness of the bucket brigade quantum random access memory model introduced by Giovannetti, Lloyd, and Maccone [Phys. Rev. Lett., 2008]. Due to a result of Regev and Schiff [ICALP, 2008], 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. 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.

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Keywords
  • Quantum Mechanics
  • Quantum Memories
  • Quantum Error Correction

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