Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems

Details Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems

2011-09-30

arxiv.org/abs/1109.6872v2

Phys. Rev. E 84, 061152 (2011)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 7 figures

Scientific paper

10.1103/PhysRevE.84.061152

We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of "typical" instances. We find that at large sizes N, the complexity increases exponentially for all models that we study. We also compare our results against the complexity of the analogous classical algorithm WalkSAT and show that the harder the problem is for the classical algorithm the harder it is also for the quantum adiabatic algorithm.

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