D. L. Shepelyansky

It is proposed to modify the Cirac-Zoller proposal of quantum computer with cold ions in a global oscillator trap potential by adding a periodic potential with an incommensurate average ratio of number of ions to number of periods being order of unity. With the increase of the periodic potential amplitude the system enters in the Aubry pinned phase characterized by quasi-frozen positions of ions and a gap of their first phonon excitations becomes independent of number of ions. This gives hopes that this quantum computer will be really scalable. It is argued that the usual single- and two-qubit gates can be realized between the nearby ions in the Aubry phase. The possibilities of experimental realizations of a periodic potential with microtrap arrays or optical lattices are discussed. It is pointed that the disorder of distances between microtraps with one ion per trap can lead to the Anderson localization of phonon modes with interesting possibilities for ion quantum computing.

We study analytically and numerically the properties of one-dimensional chain of cold ions placed in a periodic potential of optical lattice and global harmonic potential of a trap. In close similarity with the Frenkel-Kontorova model, a transition from sliding to pinned phase takes place with the increase of the optical lattice potential for the density of ions incommensurate with the lattice period. Quantum fluctuations lead to a quantum phase transition and melting of pinned instanton glass phase at large values of dimensional Planck constant. The obtained results are also relevant for a Wigner crystal placed in a periodic potential.