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 (where 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.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.
Highlights
A random access memory (RAM) is a device that stores information in an array of memory cells in the form of bits
We analyzed the robustness of the bucket brigade qRAM scheme introduced in [13, 12] under an optimistic error model
The primary advantage of the bucket brigade scheme is the need for a polynomial in n number of gate activations per memory reading
Summary
A random access memory (RAM) is a device that stores information in an array of memory cells in the form of bits. A conceptually simple physical implementation of a qRAM corresponds to a direct generalization of the fanout architecture used in classical RAMs. the number of faulty components that can be tolerated by the quantum architecture is of prime importance due to the difficulty in maintaining quantum coherence. One advantage of bucket brigade qRAM is to bypass the poly-log overhead of fault tolerant quantum error correction needed to achieve a constant error rate for a look-up. The main motivation for the quantum bucket brigade approach over a straightforward binary-tree approach is that the equivalent of the active gates are the only gates prone to error, and an inverse polynomial in n error rate suffices in order to achieve an overall constant error per qRAM look-up.
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