How to Make the Quantum Adiabatic Algorithm Fail

Details How to Make the Quantum Adiabatic Algorithm Fail How to Make the Quantum Adiabatic Algorithm Fail

2005-12-19

arxiv.org/abs/quant-ph/0512159v1

International Journal of Quantum Information, Vol. 6, No. 3 (2008), 503-516

Physics

Quantum Physics

12 pages, 2 figures

Scientific paper

The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will not find the minimum if the run time grows more slowly than square root of N. These poor choices are nonlocal and wash out any structure in the cost function to be minimized and the best that can be hoped for is Grover speedup. These failures tell us what not to do when designing quantum adiabatic algorithms.

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