Simulations of the adiabatic quantum optimization for the Set Partition Problem

Details Simulations of the adiabatic quantum optimization for the Set Partition Problem Simulations of the adiabatic quantum optimization for the Set Partition Problem

2001-12-22

arxiv.org/abs/quant-ph/0112143v2

Physics

Quantum Physics

13 pages, 5 figures Added simulation results for n=17 bits

Scientific paper

We analyze the complexity of the quantum optimization algorithm based on adiabatic evolution for the set partition problem. We introduce a cost function defined on a logarithmic scale of the partition residues so that the total number of values of the cost function is of the order of the problem size. We simulate the behavior of the algorithm by numerical solution of the time-dependent Schroedinger equation as well as the stationary equation for the adiabatic eigenvalues. The numerical results for the time-dependent quantum evolution indicate that the complexity of the algorithm scales exponentially with the problem size.This result appears to contradict the recent numerical results for complexity of quantum adiabatic algorithm applied to a different NP-complete problem (Farhi et al, Science 292, p.472 (2001)).

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