Abstract
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there is no known polynomial algorithm (classical or quantum) for the problem and yet it arises as part of a series of problems for which it being intractable would imply complexity-theoretic collapses. We give a reduction which proves that if one can efficiently evaluate the power of the unique sink orientation outmap, then there exists a polynomial time quantum algorithm for the unique sink orientation problem on cubes.
- Received 6 July 2016
DOI:https://doi.org/10.1103/PhysRevA.96.012323
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society