Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm

Details Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm

2008-03-27

arxiv.org/abs/0803.3971v2

Phys. Rev. Lett. 101, 170503 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.101.170503

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 (QAA) for much larger sizes than before. For a range of sizes, N <= 128, where the classical Davis-Putnam algorithm shows exponential median complexity, the QAA shows polynomial median complexity. The bottleneck of the algorithm is an isolated avoided crossing point of a Landau-Zener type (collision between the two lowest energy levels only).

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