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arXiv · 1710.10790

Super-exponential query complexity reduction via noise-resistant quantum search

Daniel Z. Zanger
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Abstract

In the SEARCH WITH ADVICE problem, a single entry of interest within a database of N entries is to be found assuming that an ordering of the entries, from that with the highest probability of being the entry of interest (as determined by a so-called advice distribution) to that with the lowest, is provided. We present a quantum algorithm that, in the presence of significant levels of quantum noise, solves SEARCH WITH ADVICE for a power law advice distribution with average-case query complexity O(1) as N tends to infinity. Since as we also show the best classical algorithms for this problem exhibit average-case query complexity of order no better than log(N), our quantum algorithm provides a super-exponential reduction in query complexity.

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Daniel Z. Zanger. 2017-10-30. Super-exponential query complexity reduction via noise-resistant quantum search. https://arxiv.org/abs/1710.10790

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