TOPICAL REVIEW: Optimization using quantum mechanics: quantum annealing through adiabatic evolution
Abstract
We review here some recent work in the field of quantum annealing, alias adiabatic quantum computation. The idea of quantum annealing is to perform optimization by a quantum adiabatic evolution which tracks the ground state of a suitable timedependent Hamiltonian, where 'planck' is slowly switched off. We illustrate several applications of quantum annealing strategies, starting from textbook toymodels—doublewell potentials and other onedimensional examples, with and without disorder. These examples display in a clear way the crucial differences between classical and quantum annealing. We then discuss applications of quantum annealing to challenging hard optimization problems, such as the random Ising model, the travelling salesman problem and Boolean satisfiability problems. The techniques used to implement quantum annealing are either deterministic Schrödinger's evolutions, for the toy models, or pathintegral Monte Carlo and Green's function Monte Carlo approaches, for the hard optimization problems. The crucial role played by disorder and the associated nontrivial LandauZener tunnelling phenomena is discussed and emphasized.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 September 2006
 DOI:
 10.1088/03054470/39/36/R01
 Bibcode:
 2006JPhA...39R.393S