Effect of Local Minima on Adiabatic Quantum Optimization

Details Effect of Local Minima on Adiabatic Quantum Optimization Effect of Local Minima on Adiabatic Quantum Optimization

2007-09-05

arxiv.org/abs/0709.0528v2

Phys. Rev. Lett. 100, 130503 (2008)

Physics

Quantum Physics

4 pages, published version

Scientific paper

10.1103/PhysRevLett.100.130503

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that for problems that have exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.

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