Adiabatic Quantum Computation, Entanglement-Dependent Two-Particle Holonomic Phase, Geometry Of Quantum Evolution For Mixed Quantum States, Equation Of State Of Holographic QCD Matter And The Nature Of The Chiral Transition, Ground-State Degeneracy Of Top

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 states of the interpolating Hamiltonian....

The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-418615-423003.pdf