Eigenlevel statistics of the quantum adiabatic algorithm

Details Eigenlevel statistics of the quantum adiabatic algorithm Eigenlevel statistics of the quantum adiabatic algorithm

2005-12-02

arxiv.org/abs/quant-ph/0512018v1

Phys. Rev. A 72, 052336 (2005)

Physics

Quantum Physics

8 pages, 10 ps figures

Scientific paper

10.1103/PhysRevA.72.052336

We study the eigenlevel spectrum of quantum adiabatic algorithm for 3-satisfiability problem, focusing on single-solution instances. The properties of the ground state and the associated gap, crucial for determining the running time of the algorithm, are found to be far from the predictions of random matrix theory. The distribution of gaps between the ground and the first excited state shows an abundance of small gaps. Eigenstates from the central part of the spectrum are, on the other hand, well described by random matrix theory.

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