# Size dependence of the minimum excitation gap in the quantum adiabatic algorithm.

@article{Young2008SizeDO, title={Size dependence of the minimum excitation gap in the quantum adiabatic algorithm.}, author={A. P. Young and Sergey Knysh and Vadim N. Smelyanskiy}, journal={Physical review letters}, year={2008}, volume={101 17}, pages={ 170503 } }

We study the typical (median) value of the minimum gap in the quantum version of the exact cover problem using quantum Monte Carlo simulations, in order to understand the complexity of the quantum adiabatic algorithm for much larger sizes than before. For a range of sizes N< or =128, where the classical Davis-Putnam algorithm shows exponential median complexity, the quantum adiabatic algorithm shows polynomial median complexity. The bottleneck of the algorithm is an isolated avoided-crossing… CONTINUE READING

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