Quantum computer with cold ions in the Aubry pinned phase

Abstract

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.

Properties of phonon modes of an ion-trap quantum computer in the Aubry phase

“…In fact, a configuration of a similar type had been proposed by Cirac-Zoller in [34] where a periodic potential was assumed to be created by equidistant microtraps. However, it was argued [18] that for ν = 1, even with a high periodic potential amplitude, Bloch waves will ballistically propagates through the whole periodic crystal-like structure according to the Bloch theorem [35,36]. The presence of such a Bloch wave at ν ≈ 1 is clearly seen in Fig.…”

“…Also, the coupling between ion chain and the internal ion levels drops as 1/ √ N . To avoid these scaling problems for large N , it was proposed to place ions in the Aubry pinned phase created by an additional periodic potential [18]. In the Aubry phase, the phonon excitations of the ion chain have an excitation gap independent of N that is expected to protect the accuracy of quantum gates even for N → ∞.…”

“…However, when the optical lattice amplitude K exceeds a certain critical value K c , the chain enters in the Aubry pinned phase with the appearance of an excitation gap ω g which is independent of the chain length and of the number of ions. The main properties of this charge system are described in [18,19,26,27]. However, these studies mainly addressed the transport properties of charges, while for the analysis of the robustness of the quantum gates it is necessary to understand the properties of phonon excitations of the ion chain and its response to the recoil momentum transfer from the laser pulses acting on internal ion states.…”

Thermoelectricity Modeling with Cold Dipole Atoms in Aubry Phase of Optical Lattice

“…Since such Aubry phase parameters are well accessible for experiments, it may be also interesting to test the quantum gate operations of atomic qubits, formed by two atomic levels, with dipole interaction between qubits. Such a system is similar to ion quantum computer in the Aubry phase discussed in [31]. As argued in [31], the optical gap of Aubry phase should protect gate accuracy.…”

“…Such a system is similar to ion quantum computer in the Aubry phase discussed in [31]. As argued in [31], the optical gap of Aubry phase should protect gate accuracy.…”