# A bounded-error quantum polynomial-time algorithm for two graph bisection problems

A bounded-error quantum polynomial-time algorithm for two graph bisection problems The aim of the paper was to propose a bounded-error quantum polynomial-time algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems. Given a graph with even number of vertices, the aim of the max-bisection problem is to divide the vertices into two subsets of the same size to maximize the number of edges between the two subsets, while the aim of the min-bisection problem is to minimize the number of edges between the two subsets. The proposed algorithm runs in $$O(m^2)$$ O ( m 2 ) for a graph with m edges and in the worst case runs in $$O(n^4)$$ O ( n 4 ) for a dense graph with n vertices. The proposed algorithm targets a general graph by representing both problems as Boolean constraint satisfaction problems where the set of satisfied constraints are simultaneously maximized/minimized using a novel iterative partial negation and partial measurement technique. The algorithm is shown to achieve an arbitrary high probability of success of $$1-\epsilon$$ 1 - ϵ for small $$\epsilon >0$$ ϵ > 0 using a polynomial space resources. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# A bounded-error quantum polynomial-time algorithm for two graph bisection problems

, Volume 14 (9) – Jul 14, 2015
17 pages

/lp/springer_journal/a-bounded-error-quantum-polynomial-time-algorithm-for-two-graph-ENGsFOHNsh
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1069-y
Publisher site
See Article on Publisher Site

### Abstract

The aim of the paper was to propose a bounded-error quantum polynomial-time algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems. Given a graph with even number of vertices, the aim of the max-bisection problem is to divide the vertices into two subsets of the same size to maximize the number of edges between the two subsets, while the aim of the min-bisection problem is to minimize the number of edges between the two subsets. The proposed algorithm runs in $$O(m^2)$$ O ( m 2 ) for a graph with m edges and in the worst case runs in $$O(n^4)$$ O ( n 4 ) for a dense graph with n vertices. The proposed algorithm targets a general graph by representing both problems as Boolean constraint satisfaction problems where the set of satisfied constraints are simultaneously maximized/minimized using a novel iterative partial negation and partial measurement technique. The algorithm is shown to achieve an arbitrary high probability of success of $$1-\epsilon$$ 1 - ϵ for small $$\epsilon >0$$ ϵ > 0 using a polynomial space resources.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 14, 2015

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