Quantum Adiabatic Evolution Algorithms versus Simulated Annealing

Details Quantum Adiabatic Evolution Algorithms versus Simulated Annealing Quantum Adiabatic Evolution Algorithms versus Simulated Annealing

2002-01-08

arxiv.org/abs/quant-ph/0201031v1

Physics

Quantum Physics

16pp., 10 EPS figures, using BoxedEPS macros and LaTeX. Email correspondence to E. Farhi <farhi@mit.edu>

Scientific paper

We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is treated symmetrically so the cost function depends only on the Hamming weight of the n bits. We also give two examples, closely related to these, where the similarity breaks down in that the quantum adiabatic algorithm succeeds in polynomial time whereas simulated annealing requires exponential time.

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