Quantum Lower Bound for a Tripartite Version of the Hidden Shift Problem

arXiv: Quantum Physics, Volume abs/1712.10194, 2017.

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Abstract:

In this paper, we prove a polynomial lower bound of $Omega(n^{1/3})$ on the quantum query complexity of the following rather natural generalisation of both the hidden shift and the 3-sum problem. Given an array of $3times n$ elements, is it possible to circularly shift its rows so that the sum of the elements in each column becomes zero? ...More

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