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Quantum Optimization

Does Adiabatic Quantum Optimization Truly Fail for NP-complete problems?

arXiv

Authors: Neil G. Dickson, M. H. S. Amin

Year

2010

Paper ID

11007

Status

Preprint

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~2 min

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Abstract

It has been recently argued that adiabatic quantum optimization would fail in solving NP-complete problems because of the occurrence of exponentially small gaps due to crossing of local minima of the final Hamiltonian with its global minimum near the end of the adiabatic evolution. Using perturbation expansion, we analytically show that for the NP-hard problem of maximum independent set there always exist adiabatic paths along which no such crossings occur. Therefore, in order to prove that adiabatic quantum optimization fails for any NP-complete problem, one must prove that it is impossible to find any such path in polynomial time.

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It has been recently argued that adiabatic quantum optimization would fail in solving NP-complete problems because of the occurrence of exponentially small gaps due to crossing...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1010.0669 [2] arXiv https://arxiv.org/abs/1010.0669 [3] Publisher https://arxiv.org/abs/1010.0669

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