Quantum approach to the unique sink orientation problem

Quantum approach to the unique sink orientation problem 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 kth power of the unique sink orientation outmap, then there exists a polynomial time quantum algorithm for the unique sink orientation problem on cubes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Quantum approach to the unique sink orientation problem

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Quantum approach to the unique sink orientation problem

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 kth power of the unique sink orientation outmap, then there exists a polynomial time quantum algorithm for the unique sink orientation problem on cubes.
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Publisher
The American Physical Society
Copyright
Copyright © Published by the American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.012323
Publisher site
See Article on Publisher Site

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 kth power of the unique sink orientation outmap, then there exists a polynomial time quantum algorithm for the unique sink orientation problem on cubes.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jul 18, 2017

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