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24 June 2024
 
  » arxiv » 1812.5846

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Efficient Quantum Algorithm for a Class of 2-SAT Problems
Biao Wu ; Hongye Yu ; Frank Wilczek ;
Date 14 Dec 2018
AbstractWe present an efficient quantum algorithm for a class of 2-satisfiability (2-SAT) problems. For a given 2-SAT problem, a Hamiltonian is constructed so that the solutions of the 2-SAT problem are its degenerate ground states. The key step in our algorithm is to evolve adiabatically in the subspace of the degenerate ground states. Numerically we focus on a special case that the number of Boolean variables is equal to the number of clauses. Our numerical results indicate that the time complexity of our quantum algorithm is $O(1)$ whereas its classical counterpart is $O(n)$. In the end, we point out that the adiabatic evolution in the degenerate subspace can be viewed equivalently as a quantum diffusion process in a rather randomly connected $n$-dimensional cube.
Source arXiv, 1812.5846
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