Adiabatic Quantum Computation In Satisfiability Problems, Quantum Chaos In The Quantum Computer, Quantum Chaos And Random Matrix Theory, Quantum Chaos And Imperfection Effects, Decoherence, Einselection And The Quantum Origins, Separability Of Very Noisy

Abstract

Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Michael Sipser give a quantum algorithm for solving instances of (e) the satisfiability problem, based on (e) adiabatic evolution. The evolution of the quantum state is governed by (e&eb)a time-dependent Hamiltonian that interpolates between (e&eb) an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes (e) the satisfying assignment. To ensure that the system evolves to *(e&eb) the desired final ground state, the evolution time must be (eb) big enough. Time required depends on (=) the minimum energy differences between (e&eb) the two lowest....

The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-427314-431866.pdf