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Quantum-walk speedup of backtracking algorithms. (English) Zbl 1417.68046
The author discusses quantum algorithms speedup via the technique of backtracking. To find a complete solution of a constraint satisfaction problems (CSP) backtracking algorithms explore a tree with vertices representing partial solutions of the CSP. The Davis-Putnam-Logemann-Loveland (DPLL) algorithm can be considered as a guiding example. The suggested quantum algorithms make use of an approach discussed in [A. Belovs, “Quantum walks and electric networks”, Preprint, arXiv:1302.3143] for detecting a marked vertex on a graph by a quantum walk. Some analogue of the so-called “staggered” quantum walk on a backtracking tree is used to detect the required solution.

MSC:
68Q12 Quantum algorithms and complexity in the theory of computing
05C81 Random walks on graphs
81P68 Quantum computation
Software:
BKZ; MiniSat
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