Unstructured randomness, small gaps and localization
Author(s)Farhi, Edward; Goldstone, Jeffrey; Gosset, David Nicholas; Gutmann, Sam; Shor, Peter W.
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We study the Hamiltonian associated with the quantum adiabatic algorithm with a random cost function. Because the cost function lacks structure we can prove results about the ground state. We find the ground state energy as the number of bits goes to infinity, show that the minimum gap goes to zero exponentially quickly, and we see a localization transition. We prove that there are no levels approaching the ground state near the end of the evolution. We do not know which features of this model are shared by a quantum adiabatic algorithm applied to random instances of satisfiability since despite being random they do have bit structure.
published in arxiv only per Mat Willmott.
DepartmentMassachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Department of Mathematics; Massachusetts Institute of Technology. Department of Physics
Cornell University Library
Farhi, Edward et al. "Unstructured Randomness, Small Gaps and Localization." 30 Sep 2010, arXiv.org, Cornell University Library.
Author's final manuscript