Exponential complexity of an adiabatic algorithm for an NP-complete problem

Details Exponential complexity of an adiabatic algorithm for an NP-complete problem Exponential complexity of an adiabatic algorithm for an NP-complete problem

2005-09-22

arxiv.org/abs/quant-ph/0509162v3

Phys.Rev.A. 73, 022329 (2006)

Physics

Quantum Physics

5 pages, 2 figures; v3. published version

Scientific paper

10.1103/PhysRevA.73.022329

We prove an analytical expression for the size of the gap between the ground and the first excited state of quantum adiabatic algorithm for the 3-satisfiability, where the initial Hamiltonian is a projector on the subspace complementary to the ground state. For large problem sizes the gap decreases exponentially and as a consequence the required running time is also exponential.

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